Functional Spaces for the Theory of Elliptic Partial Differential Equations (Universitext)

Demengel, Françoise; Demengel, Gilbert

ISBN 10: 1447128060 / ISBN 13: 9781447128069

Editore: Springer, 2012

Riguardo questo articolo

Codice articolo ABLIING23Mar2411530316725

Dati bibliografici

Titolo: Functional Spaces for the Theory of Elliptic...

Casa editrice: Springer

Data di pubblicazione: 2012

Legatura: Brossura

Condizione: New

Descrizione articolo

Riassunto:

As well as offering the reader a complete theory of Sobolev spaces, this volume explains how the abstract methods of convex analysis can be combined with this theory to produce existence results for the solutions of non-linear elliptic boundary problems.

Dalla quarta di copertina:

Linear and non-linear elliptic boundary problems are a fundamental subject in analysis and the spaces of weakly differentiable functions (also called Sobolev spaces) are an essential tool for analysing the regularity of its solutions.

The complete theory of Sobolev spaces is covered whilst also explaining how abstract convex analysis can be combined with this theory to produce existence results for the solutions of non-linear elliptic boundary problems. Other kinds of functional spaces are also included, useful for treating variational problems such as the minimal surface problem.

Almost every result comes with a complete and detailed proof. In some cases, more than one proof is provided in order to highlight different aspects of the result. A range of exercises of varying levels of difficulty concludes each chapter with hints to solutions for many of them.

It is hoped that this book will provide a tool for graduate and postgraduate students interested in partial differential equations, as well as a useful reference for researchers active in the field. Prerequisites include a knowledge of classical analysis, differential calculus, Banach and Hilbert spaces, integration and the related standard functional spaces, as well as the Fourier transformation on Schwartz spaces.