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Hyperbolic partial differential equations and geometric optics / Jeffrey Rauch
| Hyperbolic partial differential equations and geometric optics / Jeffrey Rauch |
| Autore | Rauch, Jeffrey |
| Pubbl/distr/stampa | Providence : American Mathematical Society, 2012 |
| Descrizione fisica | XIX, 363 p. ; 26 cm |
| Disciplina | 535'.32 |
| Collana | Graduate studies in mathematics |
| Soggetto non controllato |
Equazioni differenziali alle derivate parziali - Presentazione di ricerche
Teoria generale Equazioni della teoria elettromagnetica e dell'ottica |
| ISBN | 978-0-8218-7291-8 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-990009599370403321 |
Rauch, Jeffrey
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| Providence : American Mathematical Society, 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Hyperbolic partial differential equations and geometric optics / Jeffrey Rauch
| Hyperbolic partial differential equations and geometric optics / Jeffrey Rauch |
| Autore | Rauch, Jeffrey |
| Pubbl/distr/stampa | Providence, R. I. : American Mathematical Society, c2012 |
| Descrizione fisica | xix, 363 p. : ill. ; 27 cm |
| Disciplina | 535.32 |
| Collana | Graduate studies in mathematics, 1065-7339 ; 133 |
| Soggetto topico |
Singularities (Mathematics)
Microlocal analysis Geometrical optics - Mathematics Differential equations, Hyperbolic |
| ISBN | 9780821872918 |
| Classificazione |
AMS 35A18
AMS 35A21 AMS 35A27 AMS 35A30 AMS 35Q31 AMS 35Q60 AMS 78A05 AMS 78A60 AMS 78M35 AMS 93B07 LC QC20.7.S54R38 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991001827889707536 |
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Rauch, Jeffrey
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| Providence, R. I. : American Mathematical Society, c2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
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Partial differential equations / Jeffrey Rauch
| Partial differential equations / Jeffrey Rauch |
| Autore | RAUCH, Jeffrey |
| Pubbl/distr/stampa | New York : Springer, 1997 |
| Descrizione fisica | X, 263 p : ill. ; 25 cm |
| Disciplina | 515.353 |
| Collana | Graduate texts in mathematics |
| Soggetto topico | Equazioni differenziali alle derivate parziali |
| ISBN | 0-387-97472-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISA-990000883980203316 |
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RAUCH, Jeffrey
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| New York : Springer, 1997 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
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Partial differential equations / Jeffrey Rauch
| Partial differential equations / Jeffrey Rauch |
| Autore | Rauch, Jeffrey |
| Pubbl/distr/stampa | Springer-Verlag : New York, 1991 |
| Descrizione fisica | X, 263 p. : ill. ; 24 cm |
| Disciplina | 515.353 |
| Collana | Graduate texts in mathematics |
| Soggetto non controllato |
Partial differential equations
Equazioni differenziali parziali |
| ISBN | 0-387-97472-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-990000862570403321 |
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Rauch, Jeffrey
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| Springer-Verlag : New York, 1991 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Partial differential equations / Jeffrey Rauch
| Partial differential equations / Jeffrey Rauch |
| Autore | Rauch, Jeffrey |
| Pubbl/distr/stampa | New York [etc.] : Springer, c1991 |
| Descrizione fisica | X, 263 p. : ill. ; 25 cm. |
| Disciplina | 515.353 |
| Collana | Graduate texts in mathematics |
| Soggetto topico | Equazioni alle derivate parziali |
| ISBN | 0-387-97472-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNIBAS-000011797 |
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Rauch, Jeffrey
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| New York [etc.] : Springer, c1991 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. della Basilicata | ||
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Partial differential equations / Jeffrey Rauch
| Partial differential equations / Jeffrey Rauch |
| Autore | Rauch, Jeffrey |
| Pubbl/distr/stampa | New York, : Springer, 1991 |
| Descrizione fisica | X, 263 p. : ill. ; 25 cm. |
| Soggetto topico |
35-XX - Partial differential equations [MSC 2020]
35J25 - Boundary value problems for second-order elliptic equations [MSC 2020] 46E35 - Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems [MSC 2020] 35K05 - Heat equation [MSC 2020] 35B05 - Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs [MSC 2020] 35L05 - Wave equation [MSC 2020] 35A10 - Cauchy-Kovalevskaya theorems [MSC 2020] 35A30 - Geometric theory, characteristics, transformations in context of PDEs [MSC 2020] 35Q40 - PDEs in connection with quantum mechanics [MSC 2020] 35Dxx - Generalized solutions to partial differential equations [MSC 2020] 42B10 - Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type [MSC 2020] |
| ISBN | 978-03-87974-72-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNICAMPANIA-SUN0053134 |
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Rauch, Jeffrey
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| New York, : Springer, 1991 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
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Partial Differential Equations [[electronic resource] /] / by Jeffrey Rauch
| Partial Differential Equations [[electronic resource] /] / by Jeffrey Rauch |
| Autore | Rauch Jeffrey |
| Edizione | [1st ed. 1991.] |
| Pubbl/distr/stampa | New York, NY : , : Springer New York : , : Imprint : Springer, , 1991 |
| Descrizione fisica | 1 online resource (X, 266 p.) |
| Disciplina | 515 |
| Collana | Graduate Texts in Mathematics |
| Soggetto topico |
Mathematical analysis
Analysis (Mathematics) Analysis |
| ISBN | 1-4612-0953-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1 Power Series Methods -- §1.1. The Simplest Partial Differential Equation -- §1.2. The Initial Value Problem for Ordinary Differential Equations -- §1.3. Power Series and the Initial Value Problem for Partial Differential Equations -- §1.4. The Fully Nonlinear Cauchy—Kowaleskaya Theorem -- §1.5. Cauchy—Kowaleskaya with General Initial Surfaces -- §1.6. The Symbol of a Differential Operator -- §1.7. Holmgren’s Uniqueness Theorem -- §1.8. Fritz John’s Global Holmgren Theorem -- §1.9. Characteristics and Singular Solutions -- 2 Some Harmonic Analysis -- §2.1. The Schwartz Space $$\mathcal{J}({\mathbb{R}^d})$$ -- §2.2. The Fourier Transform on $$\mathcal{J}({\mathbb{R}^d})$$ -- §2.3. The Fourier Transform onLp$${\mathbb{R}^d}$$d):1 ?p?2 -- §2.4. Tempered Distributions -- §2.5. Convolution in $$\mathcal{J}({\mathbb{R}^d})$$ and $$\mathcal{J}'({\mathbb{R}^d})$$ -- §2.6. L2Derivatives and Sobolev Spaces -- 3 Solution of Initial Value Problems by Fourier Synthesis -- §3.1. Introduction -- §3.2. Schrödinger’s Equation -- §3.3. Solutions of Schrödinger’s Equation with Data in $$\mathcal{J}({\mathbb{R}^d})$$ -- §3.4. Generalized Solutions of Schrödinger’s Equation -- §3.5. Alternate Characterizations of the Generalized Solution -- §3.6. Fourier Synthesis for the Heat Equation -- §3.7. Fourier Synthesis for the Wave Equation -- §3.8. Fourier Synthesis for the Cauchy—Riemann Operator -- §3.9. The Sideways Heat Equation and Null Solutions -- §3.10. The Hadamard—Petrowsky Dichotomy -- §3.11. Inhomogeneous Equations, Duhamel’s Principle -- 4 Propagators andx-Space Methods -- §4.1. Introduction -- §4.2. Solution Formulas in x Space -- §4.3. Applications of the Heat Propagator -- §4.4. Applications of the Schrödinger Propagator -- §4.5. The Wave Equation Propagator ford = 1 -- §4.6. Rotation-Invariant Smooth Solutions of $${\square _{1 + 3}}\mu = 0$$ -- §4.7. The Wave Equation Propagator ford =3 -- §4.8. The Method of Descent -- §4.9. Radiation Problems -- 5 The Dirichlet Problem -- §5.1. Introduction -- §5.2. Dirichlet’s Principle -- §5.3. The Direct Method of the Calculus of Variations -- §5.4. Variations on the Theme -- §5.5.H1 the Dirichlet Boundary Condition -- §5.6. The Fredholm Alternative -- §5.7. Eigenfunctions and the Method of Separation of Variables -- §5.8. Tangential Regularity for the Dirichlet Problem -- §5.9. Standard Elliptic Regularity Theorems -- §5.10. Maximum Principles from Potential Theory -- §5.11. E. Hopf’s Strong Maximum Principles -- APPEND -- A Crash Course in Distribution Theory -- References. |
| Record Nr. | UNINA-9910479875403321 |
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Rauch Jeffrey
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| New York, NY : , : Springer New York : , : Imprint : Springer, , 1991 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Partial Differential Equations [[electronic resource] /] / by Jeffrey Rauch
| Partial Differential Equations [[electronic resource] /] / by Jeffrey Rauch |
| Autore | Rauch Jeffrey |
| Edizione | [1st ed. 1991.] |
| Pubbl/distr/stampa | New York, NY : , : Springer New York : , : Imprint : Springer, , 1991 |
| Descrizione fisica | 1 online resource (X, 266 p.) |
| Disciplina | 515 |
| Collana | Graduate Texts in Mathematics |
| Soggetto topico |
Mathematical analysis
Analysis (Mathematics) Analysis |
| ISBN | 1-4612-0953-6 |
| Classificazione |
35-01
35J05 35L05 35A10 35Exx |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1 Power Series Methods -- 1.1. The Simplest Partial Differential Equation -- 1.2. The Initial Value Problem for Ordinary Differential Equations -- 1.3. Power Series and the Initial Value Problem for Partial Differential Equations -- 1.4. The Fully Nonlinear Cauchy—Kowaleskaya Theorem -- 1.5. Cauchy—Kowaleskaya with General Initial Surfaces -- 1.6. The Symbol of a Differential Operator -- 1.7. Holmgren’s Uniqueness Theorem -- 1.8. Fritz John’s Global Holmgren Theorem -- 1.9. Characteristics and Singular Solutions -- 2 Some Harmonic Analysis -- 2.1. The Schwartz Space mathcal -- 2.2. The Fourier Transform on mathcal -- 2.3. The Fourier Transform -- 2.4. Tempered Distributions -- 2.5. Convolution -- 2.6. Derivatives and Sobolev Spaces -- 3 Solution of Initial Value Problems by Fourier Synthesis -- 3.1. Introduction -- 3.2. Schrödinger’s Equation -- 3.3. Solutions of Schrödinger’s Equation with Data -- 3.4. Generalized Solutions of Schrödinger’s Equation -- 3.5. Alternate Characterizations of the Generalized Solution -- 3.6. Fourier Synthesis for the Heat Equation -- 3.7. Fourier Synthesis for the Wave Equation -- 3.8. Fourier Synthesis for the Cauchy—Riemann Operator -- 3.9. The Sideways Heat Equation and Null Solutions -- 3.10. The Hadamard—Petrowsky Dichotomy -- 3.11. Inhomogeneous Equations, Duhamel’s Principle -- 4 Propagators and-Space Methods -- 4.1. Introduction -- 4.2. Solution Formulas in x Space -- 4.3. Applications of the Heat Propagator -- 4.4. Applications of the Schrödinger Propagator -- 4.5. The Wave Equation Propagator ford = 1 -- 4.6. Rotation-Invariant Smooth Solutions -- 4.7. The Wave Equation Propagator -- 4.8. The Method of Descent -- 4.9. Radiation Problems -- 5 The Dirichlet Problem -- 5.1. Introduction -- 5.2. Dirichlet’s Principle -- 5.3. The Direct Method of the Calculus of Variations -- 5.4. Variations on the Theme -- 5.5. H1 the Dirichlet Boundary Condition -- 5.6. The Fredholm Alternative -- 5.7. Eigenfunctions and the Method of Separation of Variables -- 5.8. Tangential Regularity for the Dirichlet Problem -- 5.9. Standard Elliptic Regularity Theorems -- 5.10. Maximum Principles from Potential Theory -- 5.11. E. Hopf’s Strong Maximum Principles -- APPEND -- A Crash Course in Distribution Theory -- References. |
| Record Nr. | UNINA-9910789219303321 |
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Rauch Jeffrey
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||
| New York, NY : , : Springer New York : , : Imprint : Springer, , 1991 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Partial Differential Equations [[electronic resource] /] / by Jeffrey Rauch
| Partial Differential Equations [[electronic resource] /] / by Jeffrey Rauch |
| Autore | Rauch Jeffrey |
| Edizione | [1st ed. 1991.] |
| Pubbl/distr/stampa | New York, NY : , : Springer New York : , : Imprint : Springer, , 1991 |
| Descrizione fisica | 1 online resource (X, 266 p.) |
| Disciplina | 515 |
| Collana | Graduate Texts in Mathematics |
| Soggetto topico |
Mathematical analysis
Analysis (Mathematics) Analysis |
| ISBN | 1-4612-0953-6 |
| Classificazione |
35-01
35J05 35L05 35A10 35Exx |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1 Power Series Methods -- 1.1. The Simplest Partial Differential Equation -- 1.2. The Initial Value Problem for Ordinary Differential Equations -- 1.3. Power Series and the Initial Value Problem for Partial Differential Equations -- 1.4. The Fully Nonlinear Cauchy—Kowaleskaya Theorem -- 1.5. Cauchy—Kowaleskaya with General Initial Surfaces -- 1.6. The Symbol of a Differential Operator -- 1.7. Holmgren’s Uniqueness Theorem -- 1.8. Fritz John’s Global Holmgren Theorem -- 1.9. Characteristics and Singular Solutions -- 2 Some Harmonic Analysis -- 2.1. The Schwartz Space mathcal -- 2.2. The Fourier Transform on mathcal -- 2.3. The Fourier Transform -- 2.4. Tempered Distributions -- 2.5. Convolution -- 2.6. Derivatives and Sobolev Spaces -- 3 Solution of Initial Value Problems by Fourier Synthesis -- 3.1. Introduction -- 3.2. Schrödinger’s Equation -- 3.3. Solutions of Schrödinger’s Equation with Data -- 3.4. Generalized Solutions of Schrödinger’s Equation -- 3.5. Alternate Characterizations of the Generalized Solution -- 3.6. Fourier Synthesis for the Heat Equation -- 3.7. Fourier Synthesis for the Wave Equation -- 3.8. Fourier Synthesis for the Cauchy—Riemann Operator -- 3.9. The Sideways Heat Equation and Null Solutions -- 3.10. The Hadamard—Petrowsky Dichotomy -- 3.11. Inhomogeneous Equations, Duhamel’s Principle -- 4 Propagators and-Space Methods -- 4.1. Introduction -- 4.2. Solution Formulas in x Space -- 4.3. Applications of the Heat Propagator -- 4.4. Applications of the Schrödinger Propagator -- 4.5. The Wave Equation Propagator ford = 1 -- 4.6. Rotation-Invariant Smooth Solutions -- 4.7. The Wave Equation Propagator -- 4.8. The Method of Descent -- 4.9. Radiation Problems -- 5 The Dirichlet Problem -- 5.1. Introduction -- 5.2. Dirichlet’s Principle -- 5.3. The Direct Method of the Calculus of Variations -- 5.4. Variations on the Theme -- 5.5. H1 the Dirichlet Boundary Condition -- 5.6. The Fredholm Alternative -- 5.7. Eigenfunctions and the Method of Separation of Variables -- 5.8. Tangential Regularity for the Dirichlet Problem -- 5.9. Standard Elliptic Regularity Theorems -- 5.10. Maximum Principles from Potential Theory -- 5.11. E. Hopf’s Strong Maximum Principles -- APPEND -- A Crash Course in Distribution Theory -- References. |
| Record Nr. | UNINA-9910828902803321 |
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Rauch Jeffrey
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| New York, NY : , : Springer New York : , : Imprint : Springer, , 1991 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Partial differential equations / Jeffrey Rauch
| Partial differential equations / Jeffrey Rauch |
| Autore | Rauch, Jeffrey |
| Pubbl/distr/stampa | New York, : Springer, 1991 |
| Descrizione fisica | X, 263 p. : ill. ; 25 cm |
| Soggetto topico |
35-XX - Partial differential equations [MSC 2020]
35J25 - Boundary value problems for second-order elliptic equations [MSC 2020] 46E35 - Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems [MSC 2020] 35K05 - Heat equation [MSC 2020] 35B05 - Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs [MSC 2020] 35L05 - Wave equation [MSC 2020] 35A10 - Cauchy-Kovalevskaya theorems [MSC 2020] 35A30 - Geometric theory, characteristics, transformations in context of PDEs [MSC 2020] 35Q40 - PDEs in connection with quantum mechanics [MSC 2020] 35Dxx - Generalized solutions to partial differential equations [MSC 2020] 42B10 - Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type [MSC 2020] |
| ISBN | 978-03-87974-72-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNICAMPANIA-VAN0053134 |
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Rauch, Jeffrey
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| New York, : Springer, 1991 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
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