E-book
Partial Differential Equations [electronic resource] / by Jürgen Jost.
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- ISBN: 9781461448099
- Physical Description: XIII, 410 p. 10 illus. online resource.
- Edition: 3rd ed. 2013.
- Publisher: New York, NY : Springer New York : 2013.
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| Subject: | Mathematics. Differential equations, partial. Mathematics. Partial Differential Equations. Theoretical, Mathematical and Computational Physics. |
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Electronic resources
| Preface | ||
| Introduction: What are Partial Differential Equations? | ||
| 1 The Laplace equation as the Prototype of an Elliptic Partial Differential Equation of Second Order | ||
| 2 The Maximum Principle | ||
| 3 Existence Techniques I: Methods Based on the Maximum Principle | ||
| 4 Existence Techniques II: Parabolic Methods. The Heat Equation | ||
| 5 Reaction-Diffusion Equations and Systems | ||
| 6 Hyperbolic Equations | ||
| 7 The Heat Equation, Semigroups, and Brownian Motion.- 8 Relationships between Different Partial Differential Equations | ||
| 9 The Dirichlet Principle. Variational Methods for the Solutions of PDEs (Existence Techniques III) | ||
| 10 Sobolev Spaces and L 2 Regularity theory | ||
| 11 Strong solutions | ||
| 12 The Regularity Theory of Schauder and the Continuity Method (Existence Techniques IV) | ||
| 13The Moser Iteration Method and the Regularity Theorem of de Giorgi and Nash | ||
| Appendix: Banach and Hilbert spaces. The L p-Spaces | ||
| References | ||
| Index of Notation | ||
| Index. |
