Partial Differential Equations
This book offers an ideal graduate-level introduction to the theory of partial differential equations. The first part of the book describes the basic mathematical problems and structures associated with elliptic, parabolic, and hyperbolic partial differential equations, and explores the connections...
| Autor principal: | |
|---|---|
| Autor Corporativo: | |
| Formato: | Libro electrónico |
| Idioma: | Inglés |
| Publicado: |
New York, NY :
Springer New York
2013.
|
| Edición: | 3rd ed |
| Colección: | Graduate Texts in Mathematics ;
214. Springer eBooks. |
| Acceso en línea: | Conectar con la versión electrónica |
| Ver en Universidad de Navarra: | https://innopac.unav.es/record=b32911166*spi |
Tabla de Contenidos:
- 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 L2̂ 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 Lp̂-Spaces
- References
- Index of Notation
- Index.
