Non-Homogeneous Boundary Value Problems and Applications: Volume III (Grundlehren Der Mathematischen Wissenschaften)

Jacques Louis Lions

ISBN 10: 3642653952 / ISBN 13: 9783642653957

Published by Springer-Verlag, 2011

About this Item

reprint edition. 326 pages. 8.98x5.98x0.71 inches. In Stock.

Seller Inventory # x-3642653952

Bibliographic Details

• Title: Non-Homogeneous Boundary Value Problems and Applications: Volume III (Grundlehren Der Mathematischen Wissenschaften)
• Publisher: Springer-Verlag
• Publication Date: 2011
• Language: English
• ISBN 10: 3642653952
• ISBN 13: 9783642653957
• Binding: Paperback
• Condition: Brand New
• Weight: 0.5 kilograms

About this title

Synopsis

1. Our essential objective is the study of the linear, non-homogeneous problems: (1) Pu = I in CD, an open set in RN, (2) fQjtl = gj on am (boundary of m), lor on a subset of the boundm"J am 1 < f < v, where Pis a linear differential operator in m and where the Q/s are linear differential operators on am. In Volumes 1 and 2, we studied, for particular c1asses of systems {P, Qj}, problem (1), (2) in c1asses of Sobolev spaces (in general constructed starting from P) of positive integer or (by interpolation) non-integer order; then, by transposition, in c1asses of Sobolev spaces of negative order, until, by passage to the limit on the order, we reached the spaces of distributions of finite order. In this volume, we study the analogous problems in spaces of inlinitely dilferentiable or analytic Itlnctions or of Gevrey-type I~mctions and by duality, in spaces 01 distribtltions, of analytic Itlnctionals or of Gevrey­ type ultra-distributions. In this manner, we obtain a c1ear vision (at least we hope so) of the various possible formulations of the boundary value problems (1), (2) for the systems {P, Qj} considered here.