Evolutionary Variational-hemivariational Inequalities: Existence and Comparison Results

Abstract

We consider an evolutionary quasilinear hemivariational inequality under constraints represented by some closed and convex subset. Our main goal is to systematically develop the method of sub-supersolution on the basis of which we then prove existence, comparison, compactness and extremality results. The obtained results are applied to a general obstacle problem. We improve the corresponding results in the recent monograph [S. Carl, V.K. Le, D. Motreanu, Nonsmooth Variational Problems and Their Inequalities. Comparison Principles and Applications, Springer Monogr. Math., Springer, New York, 2007].

Department(s)

Mathematics and Statistics

Keywords and Phrases

compactness; comparison; evolutionary variational-hemivariational inequality; extremal solution; obstacle problem; parabolic variational inequality; subsolution-supersolution

International Standard Serial Number (ISSN)

0022-247X

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2008 Elsevier, All rights reserved.

Publication Date

01 Sep 2008

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