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The Penalty Method for Variational Inequalities with Nonsmooth Unbounded Operators in Banach Space

Ya. I. Alber
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Abstract

The existence of a solution, convergence and stability of the penalty method for variational inequalities with nonsmooth unbounded uniformly and properly monotone operators in Banach spase $B$ are investigated. All the objects of the inequality - the operator A, "the right-hand part" $f$ and the set of constrains $Ω$ - are to be perturbed. The stability theorems are formulated in terms of geometric characteristics of the spaces $B$ and $B^*$. The results of this paper are continuity and generalization of the Lions' ones, published earlier in \cite{l}. They are new even in Hilbert spaces.

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BibTeXRIS

Ya. I. Alber. 1993-12-29. The Penalty Method for Variational Inequalities with Nonsmooth Unbounded Operators in Banach Space. https://arxiv.org/abs/funct-an/9312005

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