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1. We describe, at first in a very formaI manner, our essential aim. n Let m be an op en subset of R , with boundary am. In m and on am we introduce, respectively, linear differential operators P and Qj' 0 ~ i ~ 'V. By "non-homogeneous boundary value problem" we mean a problem of the following type: let f and gj' 0 ~ i ~ 'v, be given in function space s F and G , F being a space" on m" and the G/ s spaces" on am" ; j we seek u in a function space u/t "on m" satisfying (1) Pu = f in m, (2) Qju = gj on am, 0 ~ i ~ 'v«])). Qj may be identically zero on part of am, so that the number of boundary conditions may depend on the part of am considered 2. We take as "working hypothesis" that, for fEF and gjEG , j the problem (1), (2) admits a unique solution u E U/t, which depends 3 continuously on the data . But for alllinear probIems, there is a large number of choiees for the space s u/t and {F; G} (naturally linke d together). j Generally speaking, our aim is to determine families of spaces 'ft and {F; G}, associated in a "natural" way with problem (1), (2) and con j venient for applications, and also all possible choiees for u/t and {F; G} j in these families.
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Table of contents (3 chapters)
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Bibliographic Information
Book Title: Non-Homogeneous Boundary Value Problems and Applications
Book Subtitle: Vol. 1
Authors: J. L. Lions, E. Magenes
Series Title: Grundlehren der mathematischen Wissenschaften
DOI: https://doi.org/10.1007/978-3-642-65161-8
Publisher: Springer Berlin, Heidelberg
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eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag, Berlin Heidelberg 1972
Softcover ISBN: 978-3-642-65163-2Published: 15 November 2011
eBook ISBN: 978-3-642-65161-8Published: 06 December 2012
Series ISSN: 0072-7830
Series E-ISSN: 2196-9701
Edition Number: 1
Number of Pages: XVI, 360
Additional Information: Title of the original French edition: Problemes aux limites non homogenes et applications
Topics: Analysis