ENGLISH

Non-Homogeneous Boundary Value Problems and Applications: Vol. 1

By J. L. Lions , E. Magenes (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
1972
DOI
10.1007/978-3-642-65161-8
Language
english
Format
PDF
Filesize
23 MB (24491315 bytes)
Series
Die Grundlehren der mathematischen Wissenschaften 181
Edition
1
Pages
360\374
Orientation
portrait
Paginated
yes
Scanned
no
Time added
2013-11-07 16:08:46
generalMathematics

Description

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.

Similar books