Partial Differential Equations - Couverture rigide

Simon, Jacques

Couverture rigide

ISBN 10 : 1786300133 ISBN 13 : 9781786300133

Editeur : ISTE Ltd and John Wiley & Sons Inc, 2026

Synopsis

This book presents a simple and novel theory of integration, both real and vectorial, particularly suitable for the study of PDEs. This theory allows for integration with values in a Neumann space E, i.e. in which all Cauchy sequences converge, encompassing Neumann and Fréchet spaces, as well as "weak" spaces and distribution spaces.

We integrate "integrable measures", which are equivalent to "classes of integrable functions which are a.e. equals" when E is a Fréchet space. More precisely, we associate the measure f with a class f, where f(u) is the integral of fu for any test function u. The classic space Lp(Ω;E) is the set of f, and ours is the set of f; these two spaces are isomorphic.

Integration studies, in detail, for any Neumann space E, the properties of the integral and of Lp(Ω;E): regularization, image by a linear or multilinear application, change of variable, separation of multiple variables, compacts and duals. When E is a Fréchet space, we study the equivalence of the two definitions and the properties related to dominated convergence.

A propos du livre

À propos de l'auteur

Jacques Simon is Director Emeritus of Research at the CNRS, France. His research focuses on partial differential equations, particularly on the spaces used by these equations and on shape optimization.

Détails de l'édition

• Éditeur: ISTE Ltd and John Wiley & Sons Inc
• Date d'édition: 2026
• Langue: anglais
• ISBN 10: 1786300133
• ISBN 13: 9781786300133
• Reliure: Relié
• Nombre de pages: 448
• Coordonnées du fabricant: JOSSEY-BASS; https://www.wiley.com/en-us; ; 111 River Street; Hoboken; NJ; 7030; Etats-Unis
• Personne responsable: non disponible