EAN: 9783110250268

PARTIAL DIFFERENTIAL EQUATIONS - RAINER PICARD ...

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 setting (rather than on an apparently more general Banach space) 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 equation types or apply a collection of tools for
solving a variety of equations  this book takes a more global point of view by focusing on the
issues involved in determining the appropriate functional analytic setting in which a solution
theory can be naturally developed. Applications to many areas of mathematical physics are also
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 also
for researchers  who will find new results for particular evolutionary systems from
mathematical physics.

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