A Class of Variational-Hemivariational Inequalities in Reflexive Banach Spaces

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 existenc...

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Bibliographic Details
Published inJournal of elasticity Vol. 127; no. 2; pp. 151 - 178
Main Authors Migórski, Stanisław, Ochal, Anna, Sofonea, Mircea
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.04.2017
Springer Nature B.V
Springer Verlag
Subjects
Automotive Engineering
Banach space
Classical Mechanics
Contact
Convergence
Displacement
Foundations
Inequalities
Mathematical models
Mathematics
Physics
Physics and Astronomy
Uniqueness
74M10
47J22
Clarke subdifferential
Penalty operator
47J20
49J53
Frictional contact
74M15
Continuous dependence
Variational-hemivariational inequality
Existence and uniqueness
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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.
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ISSN:0374-3535
1573-2681
DOI:10.1007/s10659-016-9600-7