Title

Monotone Penalty Approximation of Extremal Solutions for Quasilinear Noncoercive Variational Inequalities

Abstract

This paper is about a monotone approximation scheme for extremal (least or greatest) solutions of the following variational inequality: u set membership, variant K: left angle bracket Au+F(u), v−uright-pointing angle bracket > or =, slanted 0, for all v set membership, variant K, in the interval between some appropriately defined sub- and supersolutions. The variational inequality is approximated by a sequence of penalty equations. The extremal solutions of the penalty equations, constructed iteratively and forming a monotone sequence, are proved to converge to the corresponding solutions of the original inequality. We note that no monotoneity assumption on the lower-order term F is imposed.

Department(s)

Mathematics and Statistics

Keywords and Phrases

extremal solutions; obstacle problems; penalty approximation; pseudomonotone operators; recession cones; sub-supersolutions; variational inequalities

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2004 Elsevier, All rights reserved.


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