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 |
Rauch Jeffrey
![]() |
||
New York, NY : , : Springer New York : , : Imprint : Springer, , 1991 | ||
![]() | ||
Lo trovi qui: Univ. Federico II | ||
|
Partial Differential Equations / / 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 |
Rauch Jeffrey
![]() |
||
New York, NY : , : Springer New York : , : Imprint : Springer, , 1991 | ||
![]() | ||
Lo trovi qui: Univ. Federico II | ||
|