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.
Recommended Citation
V. K. Le and S. Carl, "Monotone Penalty Approximation of Extremal Solutions for Quasilinear Noncoercive Variational Inequalities," Nonlinear Analysis, Elsevier, Jan 2004.
The definitive version is available at https://doi.org/10.1016/j.na.2004.02.015
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.
Publication Date
01 Jan 2004
