Evolutionary Variational-hemivariational Inequalities: Existence and Comparison Results
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].
S. Carl et al., "Evolutionary Variational-hemivariational Inequalities: Existence and Comparison Results," Journal of Mathematical Analysis and Applications, Elsevier, Sep 2008.
The definitive version is available at https://doi.org/10.1016/j.jmaa.2008.04.005
Mathematics and Statistics
Keywords and Phrases
compactness; comparison; evolutionary variational-hemivariational inequality; extremal solution; obstacle problem; parabolic variational inequality; subsolution-supersolution
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