| Titre : |
Partial differential equations |
| Type de document : |
texte imprimé |
| Auteurs : |
Jürgen Jost, Auteur |
| Editeur : |
Berlin ; London ; Cham : Springer |
| Année de publication : |
2002 |
| Collection : |
Graduate texts in mathematics |
| Importance : |
XI-325 p. |
| Présentation : |
ill. |
| Format : |
25 cm |
| ISBN/ISSN/EAN : |
978-0-387-95428-8 |
| Note générale : |
With 10 ill. Bibliogr. Index |
| Langues : |
Anglais (eng) |
| Mots-clés : |
Équations aux dérivées partielles |
| Index. décimale : |
517.911 Questions générales. Théorèmes d'existence. Théorèmes d'unicité. Différentiabilité des solutions |
| Résumé : |
This book is intended for students who wish to get an introduction to the theory of partial differential equations. The author focuses on elliptic equations and systematically develops the relevant existence schemes, always with a view towards nonlinear problems. These are maximum principle methods (particularly important for numerical analysis schemes), parabolic equations, variational methods, and continuity methods. This book also develops the main methods for obtaining estimates for solutions of elliptic equations: Sobolev space theory, weak and strong solutions, Schauder estimates, and Moser iteration. Connections between elliptic, parabolic, and hyperbolic equations are explored, as well as the connection with Brownian motion and semigroups. This book can be utilized for a one-year course on partial differential equations |
| Note de contenu : |
- Introduction The Laplace equation as the prototype of an elliptic partial differential equation of 2nd order
- The maximum principle
- Existence techniques I: methods based on the maximum principle
- Existence techniques II: Parabolic methods. The Head equation
- The wave equation and its connections with the Laplace and heat equation
- The heat equation, semigroups, and Brownian motion
- The Dirichlet principle. Variational methods for the solution of PDE (Existence techniques III)
- Sobolev spaces and L2 regularity theory
- Strong solutions
... |
Partial differential equations [texte imprimé] / Jürgen Jost, Auteur . - Berlin ; London ; Cham : Springer, 2002 . - XI-325 p. : ill. ; 25 cm. - ( Graduate texts in mathematics) . ISBN : 978-0-387-95428-8 With 10 ill. Bibliogr. Index Langues : Anglais ( eng)
| Mots-clés : |
Équations aux dérivées partielles |
| Index. décimale : |
517.911 Questions générales. Théorèmes d'existence. Théorèmes d'unicité. Différentiabilité des solutions |
| Résumé : |
This book is intended for students who wish to get an introduction to the theory of partial differential equations. The author focuses on elliptic equations and systematically develops the relevant existence schemes, always with a view towards nonlinear problems. These are maximum principle methods (particularly important for numerical analysis schemes), parabolic equations, variational methods, and continuity methods. This book also develops the main methods for obtaining estimates for solutions of elliptic equations: Sobolev space theory, weak and strong solutions, Schauder estimates, and Moser iteration. Connections between elliptic, parabolic, and hyperbolic equations are explored, as well as the connection with Brownian motion and semigroups. This book can be utilized for a one-year course on partial differential equations |
| Note de contenu : |
- Introduction The Laplace equation as the prototype of an elliptic partial differential equation of 2nd order
- The maximum principle
- Existence techniques I: methods based on the maximum principle
- Existence techniques II: Parabolic methods. The Head equation
- The wave equation and its connections with the Laplace and heat equation
- The heat equation, semigroups, and Brownian motion
- The Dirichlet principle. Variational methods for the solution of PDE (Existence techniques III)
- Sobolev spaces and L2 regularity theory
- Strong solutions
... |
|  |
Partial differential equations (2002)
