Existence and approximated results of solutions for a class of nonlocal elliptic variational-hemivariational inequalities |
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| Authors: | Yongjian Liu Zhenhai Liu Dumitru Motreanu |
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| Institution: | 1. Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin, China;2. Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Guangxi University for Nationalities, Nanning, China;3. Département de Mathématiques, Université de Perpignan, Perpignan, France |
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| Abstract: | In this paper, we consider the regularization of a class of elliptic variational-hemivariational inequalities driven by the fractional Laplace operator. First, we demonstrate characterizations of nonlocal elliptic variational-hemivariational inequalities. Next, we provide coercivity conditions that guarantee the existence and uniqueness of solution. Finally, by virtue of the so-called Browder–Tikhonov regularization method, we introduce a strongly convergent approximation procedure for the considered nonlocal problems considered without any coercivity condition. |
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| Keywords: | Browder–Tikhonov regularization method convergence results elliptic hemivariational inequalities ill-posedness nonlocal problems |
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