Joachim Gwinner, On random hemivariational inequalities: Some solvability and stability results

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DOI: 10.23952/asvao.7.2025.3.07
Volume 7, Issue 3, 1 December 2025, Pages 393-407

Abstract.This paper is concerned with various classes of parameter dependent hemivariational inequalities. First we study mixed random hemivariational inequalities and give solvability results in the Bochner-Lebesgue space $L^{\infty} (\Omega,\mu,H),$ built on a finite measure space $(\Omega,\mu)$ and a real separable Hilbert space $H$ . Next, we specialize $\Omega$ to a finite interval with Lebesgue measure and prove solvability and regularity results for extended real-valued time-dependent hemivariational inequalities. Then we focus on a probability space $(\Omega, P)$ and derive a stability result for mixed random hemivariational inequalities from a recent fundamental stability theorem. As an application, we investigate a nonsmooth boundary value problem with unilateral, friction-like, and nonmonotone boundary conditions under uncertainty and present a concrete stability result.

How to Cite this Article:
J. Gwinner, On random hemivariational inequalities: Some solvability and stability results, Appl. Set-Valued Anal. Optim. 7 (2025), 393-407.