Monotone Penalty Approximation of Extremal Solutions for Quasilinear Noncoercive Variational Inequalities
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.
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 http://dx.doi.org/10.1016/j.na.2004.02.015
Mathematics and Statistics
Keywords and Phrases
extremal solutions; obstacle problems; penalty approximation; pseudomonotone operators; recession cones; sub-supersolutions; variational inequalities
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