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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 |
Rauch Jeffrey
|
||
| 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 |
|
Rauch Jeffrey
|
||
| 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 |
|
Rauch Jeffrey
|
||
| New York, NY : , : Springer New York : , : Imprint : Springer, , 1991 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||