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We study a new class of elliptic variational-hemivariational inequalities in reflexive Banach spaces. An inequality in the class is governed by a nonlinear operator, a convex set of constraints and two nondifferentiable functionals, among which at least one is convex. We deliver a result on existence and uniqueness of a solution to the inequality. Next, we show the continuous dependence of the solution on the data of the problem and we introduce a penalty method, for which we state and prove a convergence result. Finally, we consider a mathematical model which describes the equilibrium of an elastic body in unilateral contact with a foundation. The model leads to a variational-hemivariational inequality for the displacement field, that we analyse by using our abstract results.
słowa kluczowe w j. angielskim:
variational-hemivariational inequality, existence and uniqueness, Clarke subdifferential, continuous dependence, Penalty operator, frictional contact
wydział: instytut / zakład / katedra:
Wydział Matematyki i Informatyki : Katedra Teorii Optymalizacji i Sterowania