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Numerical partial differential equations : conservation laws and elliptic equations / J. W. Thomas
| Numerical partial differential equations : conservation laws and elliptic equations / J. W. Thomas |
| Autore | Thomas, James William |
| Pubbl/distr/stampa | New York : Springer, c1999 |
| Descrizione fisica | xxii, 556 p. : ill. ; 25 cm |
| Disciplina | 515.353 |
| Collana | Texts in applied mathematics, 0939-2475 ; 33 |
| Soggetto topico |
Differential equations, Partial - Numerical solutions
Conservation laws (Mathematics) Differential equations, Elliptic |
| ISBN | 9780387983462 |
| Classificazione |
AMS 65-01
LC QA377.T4951 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991003448409707536 |
Thomas, James William
|
||
| New York : Springer, c1999 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
| ||
Oblique derivative problems for elliptic equations [[electronic resource] /] / Gary M Lieberman
| Oblique derivative problems for elliptic equations [[electronic resource] /] / Gary M Lieberman |
| Autore | Lieberman Gary M. <1952-> |
| Pubbl/distr/stampa | Singapore, : World Scientific, 2013 |
| Descrizione fisica | 1 online resource (528 p.) |
| Disciplina | 515.3533 |
| Soggetto topico |
Differential equations, Elliptic
Differential equations, Partial |
| Soggetto genere / forma | Electronic books. |
| ISBN | 981-4452-33-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; 1. Pointwise Estimates; Introduction; 1.1 The maximum principle; 1.2 The definition of obliqueness; 1.3 The case c < 0, 0 0; 1.4 A generalized change of variables formula; 1.5 The Aleksandrov-Bakel'man-Pucci maximum principles; 1.6 The interior weak Harnack inequality; 1.7 The weak Harnack inequality at the boundary; 1.8 The strong maximum principle and uniqueness; 1.9 Holder continuity; 1.10 The local maximum principle; 1.11 Pointwise estimates for solutions of mixed boundary value problems; 1.12 Derivative bounds for solutions of elliptic equations; Exercises
2. Classical Schauder Theory from a Modern PerspectiveIntroduction; 2.1 Definitions and properties of Holder spaces; 2.2 An alternative characterization of Holder spaces; 2.3 An existence result; 2.4 Basic interior estimates; 2.5 The Perron process for the Dirichlet problem; 2.6 A model mixed boundary value problem; 2.7 Domains with curved boundary; 2.8 Fredholm-Riesz-Schauder theory; Notes; Exercises; 3. The Miller Barrier and Some Supersolutions for Oblique Derivative Problems; Introduction; 3.1 Theory of ordinary differential equations; 3.2 The Miller barrier construction 3.3 Construction of supersolutions for Dirichlet data3.4 Construction of a supersolution for oblique derivative problems; 3.5 The strong maximum principle, revisited; 3.6 A Miller barrier for mixed boundary value problems; Notes; Exercises; 4. Holder Estimates for First and Second Derivatives; Introduction; 4.1 C1, estimates for continuous; 4.2 Regularized distance; 4.3 Existence of solutions for continuous; 4.4 Holder gradient estimates for the Dirichlet problem; 4.5 C1, estimates with discontinuous in two dimensions; 4.6 C1, estimates for discontinuous in higher dimensions 4.7 C2, estimatesNotes; Exercises; 5. Weak Solutions; Introduction; 5.1 Definitions and basic properties of weak derivatives; 5.2 Sobolev imbedding theorems; 5.3 Poincare's inequality; 5.4 The weak maximum principle; 5.5 Trace theorems; 5.6 Existence of weak solutions; 5.7 Higher regularity of solutions; 5.8 Global boundedness of weak solutions; 5.9 The local maximum principle; 5.10 The DeGiorgi class; 5.11 Membership of supersolutions in the De Giorgi class; 5.12 Consequences of the local estimates; 5.13 Integral characterizations of Holder spaces; 5.14 Schauder estimates; Notes; Exercises 6. Strong SolutionsIntroduction; 6.1 Pointwise estimates for strong solutions; 6.2 A sharp trace theorem; 6.3 Results from harmonic analysis; 6.4 Some further estimates for boundary value problems in a spherical cap; 6.5 Lp estimates for solutions of constant coefficient problems in a spherical cap; 6.6 Local estimates for strong solutions of constant coefficient problems; 6.7 Local interior Lp estimates for the second derivatives of strong solutions of differential equations; 6.8 Local Lp second derivative estimates near the boundary 6.9 Existence of strong solutions for the oblique derivative problem |
| Record Nr. | UNINA-9910462849403321 |
|
Lieberman Gary M. <1952->
|
||
| Singapore, : World Scientific, 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Oblique derivative problems for elliptic equations / / Gary M. Lieberman, Iowa State University, USA
| Oblique derivative problems for elliptic equations / / Gary M. Lieberman, Iowa State University, USA |
| Autore | Lieberman Gary M. <1952-> |
| Pubbl/distr/stampa | Singapore, : World Scientific, 2013 |
| Descrizione fisica | 1 online resource (xv, 509 pages) : illustrations |
| Disciplina | 515.3533 |
| Collana | Gale eBooks |
| Soggetto topico |
Differential equations, Elliptic
Mathematical physics |
| ISBN | 981-4452-33-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; 1. Pointwise Estimates; Introduction; 1.1 The maximum principle; 1.2 The definition of obliqueness; 1.3 The case c < 0, 0 0; 1.4 A generalized change of variables formula; 1.5 The Aleksandrov-Bakel'man-Pucci maximum principles; 1.6 The interior weak Harnack inequality; 1.7 The weak Harnack inequality at the boundary; 1.8 The strong maximum principle and uniqueness; 1.9 Holder continuity; 1.10 The local maximum principle; 1.11 Pointwise estimates for solutions of mixed boundary value problems; 1.12 Derivative bounds for solutions of elliptic equations; Exercises
2. Classical Schauder Theory from a Modern PerspectiveIntroduction; 2.1 Definitions and properties of Holder spaces; 2.2 An alternative characterization of Holder spaces; 2.3 An existence result; 2.4 Basic interior estimates; 2.5 The Perron process for the Dirichlet problem; 2.6 A model mixed boundary value problem; 2.7 Domains with curved boundary; 2.8 Fredholm-Riesz-Schauder theory; Notes; Exercises; 3. The Miller Barrier and Some Supersolutions for Oblique Derivative Problems; Introduction; 3.1 Theory of ordinary differential equations; 3.2 The Miller barrier construction 3.3 Construction of supersolutions for Dirichlet data3.4 Construction of a supersolution for oblique derivative problems; 3.5 The strong maximum principle, revisited; 3.6 A Miller barrier for mixed boundary value problems; Notes; Exercises; 4. Holder Estimates for First and Second Derivatives; Introduction; 4.1 C1, estimates for continuous; 4.2 Regularized distance; 4.3 Existence of solutions for continuous; 4.4 Holder gradient estimates for the Dirichlet problem; 4.5 C1, estimates with discontinuous in two dimensions; 4.6 C1, estimates for discontinuous in higher dimensions 4.7 C2, estimatesNotes; Exercises; 5. Weak Solutions; Introduction; 5.1 Definitions and basic properties of weak derivatives; 5.2 Sobolev imbedding theorems; 5.3 Poincare's inequality; 5.4 The weak maximum principle; 5.5 Trace theorems; 5.6 Existence of weak solutions; 5.7 Higher regularity of solutions; 5.8 Global boundedness of weak solutions; 5.9 The local maximum principle; 5.10 The DeGiorgi class; 5.11 Membership of supersolutions in the De Giorgi class; 5.12 Consequences of the local estimates; 5.13 Integral characterizations of Holder spaces; 5.14 Schauder estimates; Notes; Exercises 6. Strong SolutionsIntroduction; 6.1 Pointwise estimates for strong solutions; 6.2 A sharp trace theorem; 6.3 Results from harmonic analysis; 6.4 Some further estimates for boundary value problems in a spherical cap; 6.5 Lp estimates for solutions of constant coefficient problems in a spherical cap; 6.6 Local estimates for strong solutions of constant coefficient problems; 6.7 Local interior Lp estimates for the second derivatives of strong solutions of differential equations; 6.8 Local Lp second derivative estimates near the boundary 6.9 Existence of strong solutions for the oblique derivative problem |
| Record Nr. | UNINA-9910786966603321 |
|
Lieberman Gary M. <1952->
|
||
| Singapore, : World Scientific, 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Oblique derivative problems for elliptic equations / / Gary M. Lieberman, Iowa State University, USA
| Oblique derivative problems for elliptic equations / / Gary M. Lieberman, Iowa State University, USA |
| Autore | Lieberman Gary M. <1952-> |
| Pubbl/distr/stampa | Singapore, : World Scientific, 2013 |
| Descrizione fisica | 1 online resource (xv, 509 pages) : illustrations |
| Disciplina | 515.3533 |
| Collana | Gale eBooks |
| Soggetto topico |
Differential equations, Elliptic
Mathematical physics |
| ISBN | 981-4452-33-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; 1. Pointwise Estimates; Introduction; 1.1 The maximum principle; 1.2 The definition of obliqueness; 1.3 The case c < 0, 0 0; 1.4 A generalized change of variables formula; 1.5 The Aleksandrov-Bakel'man-Pucci maximum principles; 1.6 The interior weak Harnack inequality; 1.7 The weak Harnack inequality at the boundary; 1.8 The strong maximum principle and uniqueness; 1.9 Holder continuity; 1.10 The local maximum principle; 1.11 Pointwise estimates for solutions of mixed boundary value problems; 1.12 Derivative bounds for solutions of elliptic equations; Exercises
2. Classical Schauder Theory from a Modern PerspectiveIntroduction; 2.1 Definitions and properties of Holder spaces; 2.2 An alternative characterization of Holder spaces; 2.3 An existence result; 2.4 Basic interior estimates; 2.5 The Perron process for the Dirichlet problem; 2.6 A model mixed boundary value problem; 2.7 Domains with curved boundary; 2.8 Fredholm-Riesz-Schauder theory; Notes; Exercises; 3. The Miller Barrier and Some Supersolutions for Oblique Derivative Problems; Introduction; 3.1 Theory of ordinary differential equations; 3.2 The Miller barrier construction 3.3 Construction of supersolutions for Dirichlet data3.4 Construction of a supersolution for oblique derivative problems; 3.5 The strong maximum principle, revisited; 3.6 A Miller barrier for mixed boundary value problems; Notes; Exercises; 4. Holder Estimates for First and Second Derivatives; Introduction; 4.1 C1, estimates for continuous; 4.2 Regularized distance; 4.3 Existence of solutions for continuous; 4.4 Holder gradient estimates for the Dirichlet problem; 4.5 C1, estimates with discontinuous in two dimensions; 4.6 C1, estimates for discontinuous in higher dimensions 4.7 C2, estimatesNotes; Exercises; 5. Weak Solutions; Introduction; 5.1 Definitions and basic properties of weak derivatives; 5.2 Sobolev imbedding theorems; 5.3 Poincare's inequality; 5.4 The weak maximum principle; 5.5 Trace theorems; 5.6 Existence of weak solutions; 5.7 Higher regularity of solutions; 5.8 Global boundedness of weak solutions; 5.9 The local maximum principle; 5.10 The DeGiorgi class; 5.11 Membership of supersolutions in the De Giorgi class; 5.12 Consequences of the local estimates; 5.13 Integral characterizations of Holder spaces; 5.14 Schauder estimates; Notes; Exercises 6. Strong SolutionsIntroduction; 6.1 Pointwise estimates for strong solutions; 6.2 A sharp trace theorem; 6.3 Results from harmonic analysis; 6.4 Some further estimates for boundary value problems in a spherical cap; 6.5 Lp estimates for solutions of constant coefficient problems in a spherical cap; 6.6 Local estimates for strong solutions of constant coefficient problems; 6.7 Local interior Lp estimates for the second derivatives of strong solutions of differential equations; 6.8 Local Lp second derivative estimates near the boundary 6.9 Existence of strong solutions for the oblique derivative problem |
| Record Nr. | UNINA-9910814518403321 |
|
Lieberman Gary M. <1952->
|
||
| Singapore, : World Scientific, 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
On first and second order planar elliptic equations with degeneracies / / Abdelhamid Meziani
| On first and second order planar elliptic equations with degeneracies / / Abdelhamid Meziani |
| Autore | Meziani Abdelhamid <1957-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2011 |
| Descrizione fisica | 1 online resource (77 p.) |
| Disciplina | 515/.3533 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Degenerate differential equations
Differential equations, Elliptic |
| Soggetto genere / forma | Electronic books. |
| ISBN | 0-8218-8750-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Introduction""; ""Chapter 1. Preliminaries""; ""Chapter 2. Basic Solutions""; ""2.1. Properties of basic solutions""; ""2.2. The spectral equation and Spec(L0)""; ""2.3. Existence of basic solutions""; ""2.4. Properties of the fundamental matrix of (E,)""; ""2.5. The system of equations for the adjoint operator L*""; ""2.6. Continuation of a simple spectral value""; ""2.7. Continuation of a double spectral value""; ""2.8. Purely imaginary spectral value""; ""2.9. Main result about basic solutions""; ""Chapter 3. Example""
""Chapter 4. Asymptotic behavior of the basic solutions of L""""4.1. Estimate of ""; ""4.2. First estimate of and ""; ""4.3. End of the proof of Theorem 4.1""; ""Chapter 5. The kernels""; ""5.1. Two lemmas""; ""5.2. Proof of Theorem 5.1""; ""5.3. Modified kernels""; ""Chapter 6. The homogeneous equation L u=0""; ""6.1. Representation of solutions in a cylinder""; ""6.2. Cauchy integral formula""; ""6.3. Consequences""; ""Chapter 7. The nonhomogeneous equation L u=F""; ""7.1. Generalized Cauchy Integral Formula""; ""7.2. The integral operator T""; ""7.3. Compactness of the operator T"" ""Chapter 8. The semilinear equation""""Chapter 9. The second order equation: Reduction""; ""Chapter 10. The homogeneous equation Pu=0""; ""10.1. Some properties""; ""10.2. Main result about the homogeneous equation Pu=0""; ""10.3. A maximum principle""; ""Chapter 11. The nonhomogeneous equation Pu=F""; ""Chapter 12. Normalization of a Class of Second Order Equations with a Singularity ""; ""Bibliography"" |
| Record Nr. | UNINA-9910480879503321 |
|
Meziani Abdelhamid <1957->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
On first and second order planar elliptic equations with degeneracies / / Abdelhamid Meziani
| On first and second order planar elliptic equations with degeneracies / / Abdelhamid Meziani |
| Autore | Meziani Abdelhamid <1957-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2011 |
| Descrizione fisica | 1 online resource (77 p.) |
| Disciplina | 515/.3533 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Degenerate differential equations
Differential equations, Elliptic |
| ISBN | 0-8218-8750-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Introduction""; ""Chapter 1. Preliminaries""; ""Chapter 2. Basic Solutions""; ""2.1. Properties of basic solutions""; ""2.2. The spectral equation and Spec(L0)""; ""2.3. Existence of basic solutions""; ""2.4. Properties of the fundamental matrix of (E,)""; ""2.5. The system of equations for the adjoint operator L*""; ""2.6. Continuation of a simple spectral value""; ""2.7. Continuation of a double spectral value""; ""2.8. Purely imaginary spectral value""; ""2.9. Main result about basic solutions""; ""Chapter 3. Example""
""Chapter 4. Asymptotic behavior of the basic solutions of L""""4.1. Estimate of ""; ""4.2. First estimate of and ""; ""4.3. End of the proof of Theorem 4.1""; ""Chapter 5. The kernels""; ""5.1. Two lemmas""; ""5.2. Proof of Theorem 5.1""; ""5.3. Modified kernels""; ""Chapter 6. The homogeneous equation L u=0""; ""6.1. Representation of solutions in a cylinder""; ""6.2. Cauchy integral formula""; ""6.3. Consequences""; ""Chapter 7. The nonhomogeneous equation L u=F""; ""7.1. Generalized Cauchy Integral Formula""; ""7.2. The integral operator T""; ""7.3. Compactness of the operator T"" ""Chapter 8. The semilinear equation""""Chapter 9. The second order equation: Reduction""; ""Chapter 10. The homogeneous equation Pu=0""; ""10.1. Some properties""; ""10.2. Main result about the homogeneous equation Pu=0""; ""10.3. A maximum principle""; ""Chapter 11. The nonhomogeneous equation Pu=F""; ""Chapter 12. Normalization of a Class of Second Order Equations with a Singularity ""; ""Bibliography"" |
| Record Nr. | UNINA-9910788617703321 |
|
Meziani Abdelhamid <1957->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
On first and second order planar elliptic equations with degeneracies / / Abdelhamid Meziani
| On first and second order planar elliptic equations with degeneracies / / Abdelhamid Meziani |
| Autore | Meziani Abdelhamid <1957-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2011 |
| Descrizione fisica | 1 online resource (77 p.) |
| Disciplina | 515/.3533 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Degenerate differential equations
Differential equations, Elliptic |
| ISBN | 0-8218-8750-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Introduction""; ""Chapter 1. Preliminaries""; ""Chapter 2. Basic Solutions""; ""2.1. Properties of basic solutions""; ""2.2. The spectral equation and Spec(L0)""; ""2.3. Existence of basic solutions""; ""2.4. Properties of the fundamental matrix of (E,)""; ""2.5. The system of equations for the adjoint operator L*""; ""2.6. Continuation of a simple spectral value""; ""2.7. Continuation of a double spectral value""; ""2.8. Purely imaginary spectral value""; ""2.9. Main result about basic solutions""; ""Chapter 3. Example""
""Chapter 4. Asymptotic behavior of the basic solutions of L""""4.1. Estimate of ""; ""4.2. First estimate of and ""; ""4.3. End of the proof of Theorem 4.1""; ""Chapter 5. The kernels""; ""5.1. Two lemmas""; ""5.2. Proof of Theorem 5.1""; ""5.3. Modified kernels""; ""Chapter 6. The homogeneous equation L u=0""; ""6.1. Representation of solutions in a cylinder""; ""6.2. Cauchy integral formula""; ""6.3. Consequences""; ""Chapter 7. The nonhomogeneous equation L u=F""; ""7.1. Generalized Cauchy Integral Formula""; ""7.2. The integral operator T""; ""7.3. Compactness of the operator T"" ""Chapter 8. The semilinear equation""""Chapter 9. The second order equation: Reduction""; ""Chapter 10. The homogeneous equation Pu=0""; ""10.1. Some properties""; ""10.2. Main result about the homogeneous equation Pu=0""; ""10.3. A maximum principle""; ""Chapter 11. The nonhomogeneous equation Pu=F""; ""Chapter 12. Normalization of a Class of Second Order Equations with a Singularity ""; ""Bibliography"" |
| Record Nr. | UNINA-9910817273903321 |
|
Meziani Abdelhamid <1957->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
On some aspects of oscillation theory and geometry / / Bruno Bianchini, Luciano Mari, Marco Rigoli
| On some aspects of oscillation theory and geometry / / Bruno Bianchini, Luciano Mari, Marco Rigoli |
| Autore | Bianchini Bruno <1958-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2012 |
| Descrizione fisica | 1 online resource (208 p.) |
| Disciplina | 515.352 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Difference equations - Oscillation theory
Spectral theory (Mathematics) Differential equations, Elliptic |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-1056-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Chapter 1. Introduction""; ""Chapter 2. The Geometric setting""; ""2.1. Cut-locus and volume growth function""; ""2.2. Model manifolds and basic comparisons""; ""2.3. Some spectral theory on manifolds""; ""Chapter 3. Some geometric examples related to oscillation theory""; ""3.1. Conjugate points and Myers type compactness results""; ""3.2. The spectrum of the Laplacian on complete manifolds""; ""3.3. Spectral estimates and immersions""; ""3.4. Spectral estimates and nonlinear PDE""; ""Chapter 4. On the solutions of the ODE ( �)�+ =0""
""4.1. Existence, uniqueness and the behaviour of zeroes""""4.2. The critical curve: definition and main estimates""; ""Chapter 5. Below the critical curve""; ""5.1. Positivity and estimates from below""; ""5.2. Stability, index of -Î?- ( ) and the uncertainty principle""; ""5.3. A comparison at infinity for nonlinear PDE""; ""5.4. Yamabe type equations with a sign-changing nonlinearity""; ""5.5. Upper bounds for the number of zeroes of ""; ""Chapter 6. Exceeding the critical curve""; ""6.1. First zero and oscillation""; ""6.2. Comparison with known criteria"" ""6.3. Instability and index of -Î?- ( )""""6.4. Some remarks on minimal surfaces""; ""6.5. Newton operators, unstable hypersurfaces and the Gauss map""; ""6.6. Dealing with a possibly negative potential""; ""6.7. An extension of Calabi compactness criterion""; ""Chapter 7. Much above the critical curve""; ""7.1. Controlling the oscillation""; ""7.2. The growth of the index of -Î?- ( )""; ""7.3. The essential spectrum of -Î? and punctured manifolds""; ""Bibliography"" |
| Record Nr. | UNINA-9910480870103321 |
|
Bianchini Bruno <1958->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
On some aspects of oscillation theory and geometry / / Bruno Bianchini, Luciano Mari, Marco Rigoli
| On some aspects of oscillation theory and geometry / / Bruno Bianchini, Luciano Mari, Marco Rigoli |
| Autore | Bianchini Bruno <1958-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2012 |
| Descrizione fisica | 1 online resource (208 p.) |
| Disciplina | 515.352 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Difference equations - Oscillation theory
Spectral theory (Mathematics) Differential equations, Elliptic |
| ISBN | 1-4704-1056-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Chapter 1. Introduction""; ""Chapter 2. The Geometric setting""; ""2.1. Cut-locus and volume growth function""; ""2.2. Model manifolds and basic comparisons""; ""2.3. Some spectral theory on manifolds""; ""Chapter 3. Some geometric examples related to oscillation theory""; ""3.1. Conjugate points and Myers type compactness results""; ""3.2. The spectrum of the Laplacian on complete manifolds""; ""3.3. Spectral estimates and immersions""; ""3.4. Spectral estimates and nonlinear PDE""; ""Chapter 4. On the solutions of the ODE ( �)�+ =0""
""4.1. Existence, uniqueness and the behaviour of zeroes""""4.2. The critical curve: definition and main estimates""; ""Chapter 5. Below the critical curve""; ""5.1. Positivity and estimates from below""; ""5.2. Stability, index of -Î?- ( ) and the uncertainty principle""; ""5.3. A comparison at infinity for nonlinear PDE""; ""5.4. Yamabe type equations with a sign-changing nonlinearity""; ""5.5. Upper bounds for the number of zeroes of ""; ""Chapter 6. Exceeding the critical curve""; ""6.1. First zero and oscillation""; ""6.2. Comparison with known criteria"" ""6.3. Instability and index of -Î?- ( )""""6.4. Some remarks on minimal surfaces""; ""6.5. Newton operators, unstable hypersurfaces and the Gauss map""; ""6.6. Dealing with a possibly negative potential""; ""6.7. An extension of Calabi compactness criterion""; ""Chapter 7. Much above the critical curve""; ""7.1. Controlling the oscillation""; ""7.2. The growth of the index of -Î?- ( )""; ""7.3. The essential spectrum of -Î? and punctured manifolds""; ""Bibliography"" |
| Record Nr. | UNINA-9910796035203321 |
|
Bianchini Bruno <1958->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
On some aspects of oscillation theory and geometry / / Bruno Bianchini, Luciano Mari, Marco Rigoli
| On some aspects of oscillation theory and geometry / / Bruno Bianchini, Luciano Mari, Marco Rigoli |
| Autore | Bianchini Bruno <1958-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2012 |
| Descrizione fisica | 1 online resource (208 p.) |
| Disciplina | 515.352 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Difference equations - Oscillation theory
Spectral theory (Mathematics) Differential equations, Elliptic |
| ISBN | 1-4704-1056-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Chapter 1. Introduction""; ""Chapter 2. The Geometric setting""; ""2.1. Cut-locus and volume growth function""; ""2.2. Model manifolds and basic comparisons""; ""2.3. Some spectral theory on manifolds""; ""Chapter 3. Some geometric examples related to oscillation theory""; ""3.1. Conjugate points and Myers type compactness results""; ""3.2. The spectrum of the Laplacian on complete manifolds""; ""3.3. Spectral estimates and immersions""; ""3.4. Spectral estimates and nonlinear PDE""; ""Chapter 4. On the solutions of the ODE ( �)�+ =0""
""4.1. Existence, uniqueness and the behaviour of zeroes""""4.2. The critical curve: definition and main estimates""; ""Chapter 5. Below the critical curve""; ""5.1. Positivity and estimates from below""; ""5.2. Stability, index of -Î?- ( ) and the uncertainty principle""; ""5.3. A comparison at infinity for nonlinear PDE""; ""5.4. Yamabe type equations with a sign-changing nonlinearity""; ""5.5. Upper bounds for the number of zeroes of ""; ""Chapter 6. Exceeding the critical curve""; ""6.1. First zero and oscillation""; ""6.2. Comparison with known criteria"" ""6.3. Instability and index of -Î?- ( )""""6.4. Some remarks on minimal surfaces""; ""6.5. Newton operators, unstable hypersurfaces and the Gauss map""; ""6.6. Dealing with a possibly negative potential""; ""6.7. An extension of Calabi compactness criterion""; ""Chapter 7. Much above the critical curve""; ""7.1. Controlling the oscillation""; ""7.2. The growth of the index of -Î?- ( )""; ""7.3. The essential spectrum of -Î? and punctured manifolds""; ""Bibliography"" |
| Record Nr. | UNINA-9910819073203321 |
|
Bianchini Bruno <1958->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
