Grundlehren der mathematischen Wissenschaften

# Non-Homogeneous Boundary Value Problems and Applications

## Vol. 1

Authors: Lions, Jacques Louis, Magenes, Enrico

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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.

• Hilbert Theory of Trace and Interpolation Spaces

Lions, J. L. (et al.)

Pages 1-108

• Elliptic Operators, Hilbert Theory

Lions, J. L. (et al.)

Pages 109-226

• Variational Evolution Equations

Lions, J. L. (et al.)

Pages 227-308

eBook $84.99 price for USA in USD (gross) • ISBN 978-3-642-65161-8 • Digitally watermarked, DRM-free • Included format: PDF • ebooks can be used on all reading devices • Immediate eBook download after purchase Softcover$109.99
price for USA in USD
• ISBN 978-3-642-65163-2
• Free shipping for individuals worldwide
• Usually dispatched within 3 to 5 business days.

## Bibliographic Information

Bibliographic Information
Book Title
Non-Homogeneous Boundary Value Problems and Applications
Book Subtitle
Vol. 1
Authors
Translated by
Kenneth, P.
Series Title
Grundlehren der mathematischen Wissenschaften
Series Volume
181
1972
Publisher
Springer-Verlag Berlin Heidelberg
Springer-Verlag, Berlin Heidelberg
eBook ISBN
978-3-642-65161-8
DOI
10.1007/978-3-642-65161-8
Softcover ISBN
978-3-642-65163-2
Series ISSN
0072-7830
Edition Number
1
Number of Pages
XVI, 360