A Class of Variational-Hemivariational Inequalities in Reflexive Banach Spaces

作者：Migorski Stanislaw; Ochal Anna^*; Sofonea Mircea

来源：Journal of Elasticity, 2017, 127(2): 151-178.

DOI：10.1007/s10659-016-9600-7

• Variational-hemivariational inequality
• Clarke subdifferential
• Existence and uniqueness
• Continuous dependence
• Penalty operator
• Frictional contact

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.

• 出版日期2017-4