LAGRANGE MULTIPLIERS IN VARIATIONAL INEQUALITIES FOR NONLINEAR OPERATORS OF MONOTONE TYPE

摘要

We study a class of variational inequalities governed by linear or nonlinear mappings of monotone type under convex constraints in Banach spaces from the viewpoint of Lagrange multiplier approach. By introducing the Lagrange multiplier the convex constraint is set in variational inequalities and our original problems are reformulated as functional equations or inclusions. This approach often brings a more precise information about regularity of solutions and about regular approximation procedure. In this paper we shall try the Lagrange multiplier approach to abstract variational inequalities in Banach spaces and establish some new existence results. Moreover we give their applications to nonlinear elliptic partial differential inequalities.