Partial Differential Equations : : A unified Hilbert Space Approach / / Rainer Picard, Des McGhee.

• Superior document: Title is part of eBook package: De Gruyter DG Expositions in Mathematics Backlist eBook Package
• VerfasserIn: Picard, Rainer,; McGhee, Des,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2011]; ©2011
• Year of Publication: 2011
• Language: English
• Series: De Gruyter Expositions in Mathematics , 55
• Physical Description: 1 online resource (469 p.)
• Other title: Frontmatter --; Preface --; Contents --; Nomenclature --; Chapter 1 Elements of Hilbert Space Theory --; Chapter 2 Sobolev Lattices --; Chapter 3 Linear Partial Differential Equations with Constant Coefficients in Rn+1, n ∈ N --; Chapter 4 Linear Evolution Equations --; Chapter 5 Some Evolution Equations of Mathematical Physics --; Chapter 6 A “Royal Road” to Initial Boundary Value Problems of Mathematical Physics --; Conclusion --; Bibliography --; Index
• Format: Mode of access: Internet via World Wide Web.
• ISBN: 9783110250275; 9783110494969; 9783110238570; 9783110238471; 9783110637205; 9783110233544; 9783110233551; 9783110233636
• ISSN: 0938-6572
• DOI: 10.1515/9783110250275
• Access: restricted access
• Hierarchical level: Monograph
• Statement of Responsibility: Rainer Picard, Des McGhee.

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.