Dynamical and Geometric Aspects of Hamilton-Jacobi and Linearized Monge-Ampère Equations [[electronic resource] ] : VIASM 2016 / / by Nam Q. Le, Hiroyoshi Mitake, Hung V. Tran ; edited by Hiroyoshi Mitake, Hung V. Tran |
Autore | Le Nam Q |
Edizione | [1st ed. 2017.] |
Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017 |
Descrizione fisica | 1 online resource (VII, 228 p. 16 illus., 1 illus. in color.) |
Disciplina | 515.353 |
Collana | Lecture Notes in Mathematics |
Soggetto topico |
Partial differential equations
Calculus of variations Differential geometry Partial Differential Equations Calculus of Variations and Optimal Control; Optimization Differential Geometry |
ISBN | 3-319-54208-7 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto |
Intro -- Preface -- Contents -- Part I The Second Boundary Value Problem of the Prescribed Affine Mean Curvature Equation and Related Linearized Monge-Ampère Equation -- Introduction -- Notation -- 1 The Affine Bernstein and Boundary Value Problems -- 1.1 The Affine Bernstein and Boundary Value Problems -- 1.1.1 Minimal Graph -- 1.1.2 Affine Maximal Graph -- 1.1.3 The Affine Bernstein Problem -- 1.1.4 Connection with the Constant Scalar Curvature Problem -- 1.1.5 The First Boundary Value Problem -- 1.1.6 The Second Boundary Value Problem of the Prescribed Affine Mean Curvature Equation -- 1.1.7 Solvability of the Second Boundary Value Problem -- 1.2 Existence of Solution to the Second Boundary Value Problem -- 1.2.1 Existence of Solution via Degree Theory and A Priori Estimates -- 1.2.2 Several Boundary Regularity Results for Monge-Ampère and Linearized Monge-Ampère Equations -- 1.3 Proof of Global W4,p and C4,α Estimates -- 1.3.1 Test Functions -- 1.3.2 L1 Bound and Lower Bound on the Hessian Determinant -- 1.3.3 Gradient Bound -- 1.3.4 Legendre Transform and Upper Bound on Hessian Determinant -- References -- 2 The Linearized Monge-Ampère Equation -- 2.1 The Linearized Monge-Ampère Equation and Interior Regularity of Its Solution -- 2.1.1 The Linearized Monge-Ampère Equation -- 2.1.2 Linearized Monge-Ampère Equations in Contexts -- 2.1.3 Difficulties and Expected Regularity -- 2.1.4 Affine Invariance Property -- 2.1.5 Krylov-Safonov's Harnack Inequality -- 2.1.6 Harnack Inequality for the Linearized Monge-Ampère Equation -- 2.2 Interior Harnack and Hölder Estimates for Linearized Monge-Ampère -- 2.2.1 Proof of Caffarelli-Gutiérrez's Harnack Inequality -- 2.2.2 Proof of the Interior Hölder Estimates for the Inhomogeneous Linearized Monge-Ampère Equation -- 2.3 Global Hölder Estimates for the Linearized Monge-Ampère Equations.
2.3.1 Boundary Hölder Continuity for Solutions of Non-uniformly Elliptic Equations -- 2.3.2 Savin's Localization Theorem -- 2.3.3 Proof of Global Hölder Estimates for the Linearized Monge-Ampère Equation -- References -- 3 The Monge-Ampère Equation -- 3.1 Maximum Principles and Sections of the Monge-Ampère Equation -- 3.1.1 Basic Definitions -- 3.1.2 Examples and Properties of the Normal Mapping and the Monge-Ampère Measure -- 3.1.3 Maximum Principles -- 3.1.4 John's Lemma -- 3.1.5 Comparison Principle and Applications -- 3.1.6 The Dirichlet Problem and Perron's Method -- 3.1.7 Sections of Convex Functions -- 3.2 Geometry of Sections of Solutions to the Monge-Ampère Equation -- 3.2.1 Compactness of Solutions to the Monge-Ampère Equation -- 3.2.2 Caffarelli's Localization Theorem -- 3.2.3 Strict Convexity and C1,α Estimates -- 3.2.4 Engulfing Property of Sections -- Appendix A: Auxiliary Lemmas -- Appendix B: A Heuristic Explanation of Trudinger-Wang's Non-smooth Example -- References -- Part II Dynamical Properties of Hamilton-Jacobi Equations via the Nonlinear Adjoint Method: Large Time Behavior and Discounted Approximation -- Introduction -- Notations -- References -- 4 Ergodic Problems for Hamilton-Jacobi Equations -- 4.1 Motivation -- 4.2 Existence of Solutions to Ergodic Problems -- References -- 5 Large Time Asymptotics of Hamilton-Jacobi Equations -- 5.1 A Brief Introduction -- 5.2 First-Order Case with Separable Hamiltonians -- 5.2.1 First Example -- 5.2.2 Second Example -- 5.3 First-Order Case with General Hamiltonians -- 5.3.1 Formal Calculation -- 5.3.2 Regularizing Process -- 5.3.3 Conservation of Energy and a Key Observation -- 5.3.4 Proof of Key Estimates -- 5.4 Degenerate Viscous Case -- 5.5 Asymptotic Profile of the First-Order Case -- 5.6 Viscous Case -- 5.7 Some Other Directions and Open Questions -- References. 6 Selection Problems in the Discounted Approximation Procedure -- 6.1 Selection Problems -- 6.1.1 Examples on Nonuniqueness of Ergodic Problems -- 6.1.2 Discounted Approximation -- 6.2 Regularizing Process -- 6.2.1 Regularizing Process and Construction of M -- 6.2.2 Stochastic Mather Measures -- 6.2.3 Key Estimates -- 6.3 Proof of Theorem 6.5 -- 6.4 Proof of the Commutation Lemma -- 6.5 Applications -- 6.5.1 Limit of u in Example 6.1 -- 6.5.2 Limit of u in Examples 6.3, 6.4 -- 6.6 Some Other Directions and Open Questions -- 6.6.1 Discounted Approximation Procedure -- 6.6.2 Vanishing Viscosity Procedure -- 6.6.3 Selection of Mather Measures -- References -- 7 Appendix of Part II -- 7.1 Motivation and Examples -- 7.1.1 Front Propagation Problems -- 7.1.2 Optimal Control Problems -- 7.1.2.1 Inviscid Cases -- 7.1.2.2 Viscous Cases -- 7.2 Definitions -- 7.3 Consistency -- 7.4 Comparison Principle and Uniqueness -- 7.5 Stability -- 7.6 Lipschitz Estimates -- 7.7 The Perron Method -- References. |
Record Nr. | UNISA-996466643603316 |
Le Nam Q | ||
Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017 | ||
Materiale a stampa | ||
Lo trovi qui: Univ. di Salerno | ||
|
Dynamical and Geometric Aspects of Hamilton-Jacobi and Linearized Monge-Ampère Equations [[electronic resource] ] : VIASM 2016 / / by Nam Q. Le, Hiroyoshi Mitake, Hung V. Tran ; edited by Hiroyoshi Mitake, Hung V. Tran |
Autore | Le Nam Q |
Edizione | [1st ed. 2017.] |
Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017 |
Descrizione fisica | 1 online resource (VII, 228 p. 16 illus., 1 illus. in color.) |
Disciplina | 515.353 |
Collana | Lecture Notes in Mathematics |
Soggetto topico |
Partial differential equations
Calculus of variations Differential geometry Partial Differential Equations Calculus of Variations and Optimal Control; Optimization Differential Geometry |
ISBN | 3-319-54208-7 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto |
Intro -- Preface -- Contents -- Part I The Second Boundary Value Problem of the Prescribed Affine Mean Curvature Equation and Related Linearized Monge-Ampère Equation -- Introduction -- Notation -- 1 The Affine Bernstein and Boundary Value Problems -- 1.1 The Affine Bernstein and Boundary Value Problems -- 1.1.1 Minimal Graph -- 1.1.2 Affine Maximal Graph -- 1.1.3 The Affine Bernstein Problem -- 1.1.4 Connection with the Constant Scalar Curvature Problem -- 1.1.5 The First Boundary Value Problem -- 1.1.6 The Second Boundary Value Problem of the Prescribed Affine Mean Curvature Equation -- 1.1.7 Solvability of the Second Boundary Value Problem -- 1.2 Existence of Solution to the Second Boundary Value Problem -- 1.2.1 Existence of Solution via Degree Theory and A Priori Estimates -- 1.2.2 Several Boundary Regularity Results for Monge-Ampère and Linearized Monge-Ampère Equations -- 1.3 Proof of Global W4,p and C4,α Estimates -- 1.3.1 Test Functions -- 1.3.2 L1 Bound and Lower Bound on the Hessian Determinant -- 1.3.3 Gradient Bound -- 1.3.4 Legendre Transform and Upper Bound on Hessian Determinant -- References -- 2 The Linearized Monge-Ampère Equation -- 2.1 The Linearized Monge-Ampère Equation and Interior Regularity of Its Solution -- 2.1.1 The Linearized Monge-Ampère Equation -- 2.1.2 Linearized Monge-Ampère Equations in Contexts -- 2.1.3 Difficulties and Expected Regularity -- 2.1.4 Affine Invariance Property -- 2.1.5 Krylov-Safonov's Harnack Inequality -- 2.1.6 Harnack Inequality for the Linearized Monge-Ampère Equation -- 2.2 Interior Harnack and Hölder Estimates for Linearized Monge-Ampère -- 2.2.1 Proof of Caffarelli-Gutiérrez's Harnack Inequality -- 2.2.2 Proof of the Interior Hölder Estimates for the Inhomogeneous Linearized Monge-Ampère Equation -- 2.3 Global Hölder Estimates for the Linearized Monge-Ampère Equations.
2.3.1 Boundary Hölder Continuity for Solutions of Non-uniformly Elliptic Equations -- 2.3.2 Savin's Localization Theorem -- 2.3.3 Proof of Global Hölder Estimates for the Linearized Monge-Ampère Equation -- References -- 3 The Monge-Ampère Equation -- 3.1 Maximum Principles and Sections of the Monge-Ampère Equation -- 3.1.1 Basic Definitions -- 3.1.2 Examples and Properties of the Normal Mapping and the Monge-Ampère Measure -- 3.1.3 Maximum Principles -- 3.1.4 John's Lemma -- 3.1.5 Comparison Principle and Applications -- 3.1.6 The Dirichlet Problem and Perron's Method -- 3.1.7 Sections of Convex Functions -- 3.2 Geometry of Sections of Solutions to the Monge-Ampère Equation -- 3.2.1 Compactness of Solutions to the Monge-Ampère Equation -- 3.2.2 Caffarelli's Localization Theorem -- 3.2.3 Strict Convexity and C1,α Estimates -- 3.2.4 Engulfing Property of Sections -- Appendix A: Auxiliary Lemmas -- Appendix B: A Heuristic Explanation of Trudinger-Wang's Non-smooth Example -- References -- Part II Dynamical Properties of Hamilton-Jacobi Equations via the Nonlinear Adjoint Method: Large Time Behavior and Discounted Approximation -- Introduction -- Notations -- References -- 4 Ergodic Problems for Hamilton-Jacobi Equations -- 4.1 Motivation -- 4.2 Existence of Solutions to Ergodic Problems -- References -- 5 Large Time Asymptotics of Hamilton-Jacobi Equations -- 5.1 A Brief Introduction -- 5.2 First-Order Case with Separable Hamiltonians -- 5.2.1 First Example -- 5.2.2 Second Example -- 5.3 First-Order Case with General Hamiltonians -- 5.3.1 Formal Calculation -- 5.3.2 Regularizing Process -- 5.3.3 Conservation of Energy and a Key Observation -- 5.3.4 Proof of Key Estimates -- 5.4 Degenerate Viscous Case -- 5.5 Asymptotic Profile of the First-Order Case -- 5.6 Viscous Case -- 5.7 Some Other Directions and Open Questions -- References. 6 Selection Problems in the Discounted Approximation Procedure -- 6.1 Selection Problems -- 6.1.1 Examples on Nonuniqueness of Ergodic Problems -- 6.1.2 Discounted Approximation -- 6.2 Regularizing Process -- 6.2.1 Regularizing Process and Construction of M -- 6.2.2 Stochastic Mather Measures -- 6.2.3 Key Estimates -- 6.3 Proof of Theorem 6.5 -- 6.4 Proof of the Commutation Lemma -- 6.5 Applications -- 6.5.1 Limit of u in Example 6.1 -- 6.5.2 Limit of u in Examples 6.3, 6.4 -- 6.6 Some Other Directions and Open Questions -- 6.6.1 Discounted Approximation Procedure -- 6.6.2 Vanishing Viscosity Procedure -- 6.6.3 Selection of Mather Measures -- References -- 7 Appendix of Part II -- 7.1 Motivation and Examples -- 7.1.1 Front Propagation Problems -- 7.1.2 Optimal Control Problems -- 7.1.2.1 Inviscid Cases -- 7.1.2.2 Viscous Cases -- 7.2 Definitions -- 7.3 Consistency -- 7.4 Comparison Principle and Uniqueness -- 7.5 Stability -- 7.6 Lipschitz Estimates -- 7.7 The Perron Method -- References. |
Record Nr. | UNINA-9910257380003321 |
Le Nam Q | ||
Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017 | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|
Dynamical systems IV : symplectic geometry and its applications / V. I. Arnold, S. P. Novikov (eds.) |
Edizione | [2nd, expanded and rev. ed.] |
Pubbl/distr/stampa | Berlin ; New York : Springer, c2001 |
Descrizione fisica | 335 p. : ill. ; 24 cm |
Disciplina | 516.362 |
Altri autori (Persone) |
Arnold, Vladimir Igorevic
Novikov, Sergei Petrovichauthor |
Collana | Encyclopaedia of mathematical sciences, 0938-0396 ; 4 |
Soggetto topico |
Differential geometry
Symplectic manifolds |
ISBN | 3540626352 |
Classificazione |
AMS 00A20
AMS 58F05 AMS 58F06 AMS 58F07 AMS 70H |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Record Nr. | UNISALENTO-991000837499707536 |
Berlin ; New York : Springer, c2001 | ||
Materiale a stampa | ||
Lo trovi qui: Univ. del Salento | ||
|
Einfuhrung in die Differentialgeometrie / von Wilhelm Blaschke und Hans Reichardt |
Autore | Blaschke, Wilhelm |
Edizione | [2te Aufl] |
Pubbl/distr/stampa | Berlin : Springer-Verlag, 1960 |
Descrizione fisica | 173 p. ill. ; 24 cm. |
Disciplina | 516.36 |
Collana | Grundlehren der mathematischen Wissenschaften = A series of comprehensive studies in mathematics, 0072-7830 ; 58 |
Soggetto topico | Differential geometry |
Classificazione | AMS 53-XX |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | ger |
Record Nr. | UNISALENTO-991000843149707536 |
Blaschke, Wilhelm | ||
Berlin : Springer-Verlag, 1960 | ||
Materiale a stampa | ||
Lo trovi qui: Univ. del Salento | ||
|
Einstein’s Field Equations and Their Physical Implications [[electronic resource] ] : Selected Essays in Honour of Jürgen Ehlers / / edited by Bernd G. Schmidt |
Edizione | [1st ed. 2000.] |
Pubbl/distr/stampa | Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2000 |
Descrizione fisica | 1 online resource (XIII, 433 p.) |
Disciplina | 530.11 |
Collana | Lecture Notes in Physics |
Soggetto topico |
Differential geometry
Gravitation Physics Differential Geometry Classical and Quantum Gravitation, Relativity Theory Mathematical Methods in Physics |
ISBN | 3-540-46580-4 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | Selected Solutions of Einstein’s Field Equations: Their Role in General Relativity and Astrophysics -- The Cauchy Problem for the Einstein Equations -- Post-Newtonian Gravitational Radiation -- Duality and Hidden Symmetries in Gravitational Theories -- Time-Independent Gravitational Fields -- Gravitational Lensing from a Geometric Viewpoint. |
Record Nr. | UNINA-9910139813603321 |
Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2000 | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|
Einstein’s Field Equations and Their Physical Implications [[electronic resource] ] : Selected Essays in Honour of Jürgen Ehlers / / edited by Bernd G. Schmidt |
Edizione | [1st ed. 2000.] |
Pubbl/distr/stampa | Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2000 |
Descrizione fisica | 1 online resource (XIII, 433 p.) |
Disciplina | 530.11 |
Collana | Lecture Notes in Physics |
Soggetto topico |
Differential geometry
Gravitation Physics Differential Geometry Classical and Quantum Gravitation, Relativity Theory Mathematical Methods in Physics |
ISBN | 3-540-46580-4 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | Selected Solutions of Einstein’s Field Equations: Their Role in General Relativity and Astrophysics -- The Cauchy Problem for the Einstein Equations -- Post-Newtonian Gravitational Radiation -- Duality and Hidden Symmetries in Gravitational Theories -- Time-Independent Gravitational Fields -- Gravitational Lensing from a Geometric Viewpoint. |
Record Nr. | UNISA-996466685503316 |
Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2000 | ||
Materiale a stampa | ||
Lo trovi qui: Univ. di Salerno | ||
|
Elementare differentialgeometrie / W. Blaschke, K. Leichtweiss |
Autore | Blaschke, Wilhelm |
Edizione | [5. voll. neubearb. aufl.] |
Pubbl/distr/stampa | Berlin : Springer-Verlag, 1973 |
Descrizione fisica | x, 369 p. ; 24 cm. |
Disciplina | 516.36 |
Altri autori (Persone) | Leichtweiss, K. |
Collana | Grundlehren der mathematischen Wissenschaften = A series of comprehensive studies in mathematics, 0072-7830 ; 1 |
Soggetto topico |
Differential geometry
Differential geometry-textbooks |
ISBN | 3540058893 |
Classificazione |
AMS 53-01
AMS 53-XX |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | ger |
Record Nr. | UNISALENTO-991000845709707536 |
Blaschke, Wilhelm | ||
Berlin : Springer-Verlag, 1973 | ||
Materiale a stampa | ||
Lo trovi qui: Univ. del Salento | ||
|
Elementary differential geometry / Barrett O'Neill |
Autore | O'Neill, Barrett |
Pubbl/distr/stampa | New York : Academic Press, c1966 |
Descrizione fisica | viii, 409 p. ; 24 cm |
Disciplina | 516.3602 |
Soggetto topico | Differential geometry |
Classificazione |
AMS 53-01
AMS 53-XX |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Record Nr. | UNISALENTO-991000846929707536 |
O'Neill, Barrett | ||
New York : Academic Press, c1966 | ||
Materiale a stampa | ||
Lo trovi qui: Univ. del Salento | ||
|
Elementary differential geometry / Andrew Pressley |
Autore | Pressley, Andrew |
Pubbl/distr/stampa | London : Springer-Verlag, c2001 |
Descrizione fisica | ix, 332 p. : ill. ; 24 cm |
Disciplina | 516.36 |
Collana | Springer undergraduate mathematics series, 1615-2085 |
Soggetto topico |
Differential geometry
Mathematics and statistics-textbooks |
ISBN | 1852331526 |
Classificazione |
AMS 53-01
LC QA641.P68 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Record Nr. | UNISALENTO-991003677089707536 |
Pressley, Andrew | ||
London : Springer-Verlag, c2001 | ||
Materiale a stampa | ||
Lo trovi qui: Univ. del Salento | ||
|
Elementary Symplectic Topology and Mechanics [[electronic resource] /] / by Franco Cardin |
Autore | Cardin Franco |
Edizione | [1st ed. 2015.] |
Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015 |
Descrizione fisica | 1 online resource (237 p.) |
Disciplina |
510
515.64 516.36 530.15 |
Collana | Lecture Notes of the Unione Matematica Italiana |
Soggetto topico |
Mathematical physics
Differential geometry Calculus of variations Mathematical Physics Differential Geometry Calculus of Variations and Optimal Control; Optimization |
ISBN | 3-319-11026-8 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | Beginning -- Notes on Differential Geometry -- Symplectic Manifolds -- Poisson brackets environment -- Cauchy Problem for H-J equations -- Calculus of Variations and Conjugate Points -- Asymptotic Theory of Oscillating Integrals -- Lusternik-Schnirelman and Morse -- Finite Exact Reductions -- Other instances -- Bibliography. |
Record Nr. | UNINA-9910299778503321 |
Cardin Franco | ||
Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015 | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|