a unified Hilbert space approach
Edición de la obra Partial differential equations
| Autor | R. H. Picard |
|---|---|
| Editorial | De Gruyter |
| Fecha de publicación | 2011 |
| Lugar | Berlin, New York |
| Idioma | inglés |
| Páginas | 469 |
| ISBN-13 | 9783110250268 |
| OCLC | 705567992 |
| LCCN | 2011004423 |
| Serie | De Gruyter expositions in mathematics -- 55 |
| Número de Cutter | P586p |
This book presents a systematic approach to a solution theory for linear partial differential equations developed in a Hilbert space setting based on a Sobolev Lattice structure, a simple extension of the well established notion of a chain (or scale) of Hilbert spaces. The focus on a Hilbert space (rather than an apparently more general Banach space) setting is not a severe constraint, but rather a highly adaptable and suitable approach providing a more transparent framework for presenting the main issues in the development of a solution theory for partial differential equations. In contrast to other texts on partial differential equations which consider either specific types of partial differential equations or apply a collection of tools for solving a variety of partial differential equations, this book takes a more global point of view by focussing on the issues involved in determining the appropriate functional analytic setting in which a solution theory can naturally be developed. Applications to many areas of mathematical physics are presented. The book aims to be largely self-contained. Full proofs to all but the most straightforward results are provided, keeping to a minimum references to other literature for essential material. It is therefore highly suitable as a resource for graduate courses and for researchers, who will find new results for particular evolutionary system from mathematical physics.