Nonlocal elliptic variational-hemivariational inequalities

Stanisław Migórski; Van Thien Nguyen; Shengda Zeng

doi:10.1216/JIE.2020.32.51

Abstract

We examine the existence of a weak solution to a class of variational-hemivariational inequalities governed by a fractional Laplace operator. Moreover, an existence result is proved for a bilateral obstacle problem for a nonlocal hemivariational inequality. Our approach is based on a surjectivity result for pseudomonotone mappings, properties of Clarke’s subgradient, and the Moreau–Yosida approximation.

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Stanisław Migórski. Van Thien Nguyen. Shengda Zeng. "Nonlocal elliptic variational-hemivariational inequalities." J. Integral Equations Applications 32 (1) 51 - 58, Spring 2020. https://doi.org/10.1216/JIE.2020.32.51

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Received: 6 March 2018; Accepted: 8 April 2019; Published: Spring 2020

First available in Project Euclid: 25 June 2020

zbMATH: 07223722

MathSciNet: MR4115971

Digital Object Identifier: 10.1216/JIE.2020.32.51

Subjects:

Primary: 00A05 , 35R11 , 49J52

Keywords: bilateral obstacle , Clarke subdifferential , fractional Laplace operator , Moreau–Yosida approximation , nonlocal variational-hemivariational inequality , pseudomonotone

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