Partial Differential Equations: A unified Hilbert Space Approach: 55 (De Gruyter Expositions in Mathematics, 55) - Tapa dura

Acerca del autor

Rainer Picard, Dresden University of Technology, Germany; Des McGhee, University of Strathclyde, Glasgow, Scotland, UK.

De la contraportada

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 a 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.