Tykhonov well-posedness of elliptic variational-hemivariational inequalities
Date
2019-05-10
Authors
Sofonea, Mircea
Xiao, Yi-Bin
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We consider a class of elliptic variational-hemivariational inequalities in an abstract Banach space for which we introduce the concept of well-posedness in the sense of Tykhonov. We characterize the well-posedness in terms of metric properties of a family of associated sets. Our results, which provide necessary and sufficient conditions for the well-posedness of inequalities under consideration, are valid under mild assumptions on the data. Their proofs are based on arguments of monotonicity, lower semicontinuity and properties of the Clarke directional derivative. For well-posed inequalities we also prove a continuous dependence result of the solution with respect to the data. We illustrate our abstract results in the study of one-dimensional examples, then we focus on some relevant particular cases, including variational-hemivariational inequalities with strongly monotone operators. Finally, we consider a model variational-hemivariational inequality which arises in Contact Mechanics for which we discuss its well-posedness and provide the corresponding mechanical interpretations.
Description
Keywords
Tykhonov well-posedness, Variational-hemivariational inequality, Approximating sequence, Contact problem, Unilateral constraint, Friction
Citation
Sofonea, M., & Xiao, Y. B. (2019). Tykhonov well-posedness of elliptic variational-hemivariational inequalities. <i>Electronic Journal of Differential Equations, 2019</i>(64), pp. 1-19.
Rights
Attribution 4.0 International