Partial differential equations [[electronic resource] ] : a unified Hilbert space approach / / Rainer Picard, Des McGhee

• Record Nr.: UNINA9910456578403321
• Autore: Picard R. H (Rainer H.)
• Pubbl/distr/stampa: Berlin ; ; New York, : De Gruyter, c2011
• ISBN: 1-283-39993-8; 9786613399939; 3-11-025027-6
• Descrizione fisica: 1 online resource (488 p.)
• Collana: De Gruyter expositions in mathematics, , 0938-6572 ; ; 55
• Altri autori (Persone): McGheeD. F
• Disciplina: 515/.733
• Soggetti: Hilbert space; Differential equations, Partial; Electronic books.
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 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
• Sommario/riassunto: 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.