Joachim Gwinner, On a class of mixed random variational inequalities, Vol. 2024 (2024), Article ID 22, pp. 1-15

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DOI: 10.23952/cot.2024.22

Received September 20, 2023; Accepted November 29, 2023; Published online March 26, 2024

Abstract. This paper is concerned with a class of mixed random variational inequalities that involve a $\omega$ -dependent bilinear form and a $\omega$ -dependent convex function on a convex constraint set. Measurable solvability results for variational inequalities in $\omega$ -pointwise and in $\Omega$ -integrated form are presented under coercivity assumptions. Moreover a stability result with respect to Mosco convergence is provided that is based on an abstract (deterministic) stability result of its own interest. For illustration of the presented theory a non-smooth random boundary value problem is considered that captures all the difficulties of Tresca frictional unilateral problems that result in unilateral boundary conditions and a non-smooth convex sublinear functional.

How to Cite this Article:
J. Gwinner, On a class of mixed random variational inequalities, Commun. Optim. Theory 2024 (2024) 22.