A class of variational-hemivariational inequalities in reflexive Banach spaces. (English) Zbl 1368.47045
Summary: 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.
MSC:
| 47J20 | Variational and other types of inequalities involving nonlinear operators (general) |
| 47J22 | Variational and other types of inclusions |
| 49J53 | Set-valued and variational analysis |
| 74M10 | Friction in solid mechanics |
| 74M15 | Contact in solid mechanics |
Keywords:
variational-hemivariational inequality; Clarke subdifferential; existence and uniqueness; continuous dependence; penalty operator; frictional contactReferences:
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