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

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

1993-12-29

arxiv.org/abs/funct-an/9312005v1

Mathematics

Functional Analysis

14 pages, LaTex

Scientific paper

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 $\Omega $ - 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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