Partial Differential Equations - A unified Hilbert Space Approach

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.

About the author

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

Product details

• Authors: Des McGhee, Raine Picard, Rainer Picard
• Publisher: De Gruyter
• Languages: English
• Product format: Hardback
• Released: 27.06.2011
• EAN: 9783110250268
• ISBN: 978-3-11-025026-8
• No. of pages: 469
• Dimensions: 176 mm x 32 mm x 240 mm
• Weight: 948 g
• Series: De Gruyter Expositions in Mathematics; Gruyter Expositions in Mathematics; De Gruyter Expositions in Mathematics; ISSN
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Analysis; Differenzialrechnung, Analysis / Funktionalanalysis, Funktionalanalysis, Gleichung / Differenzialgleichung, Differenzialgleichung, Funktionalanalysis und Abwandlungen, MATHEMATICS / Differential Equations / General, MATHEMATICS / Functional Analysis, MATHEMATICS / Mathematical Analysis, Advanced