Minimization principles for elliptic hemivariational inequalities

• Published in: Nonlinear analysis: real world applications Vol. 54; p. 103114
• Main Author: Han, Weimin
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Ltd 01.08.2020; Elsevier BV
• Subjects: Equivalence; Hemivariational inequality; Inequalities; Inequality; Mechanics (physics); Minimization principle; Numerical analysis; Optimization; Principles; Variational–hemivariational inequality; Hemivariational inequality; Minimization principle; Variational–hemivariational inequality
• ISSN: 1468-1218; 1878-5719
• DOI: 10.1016/j.nonrwa.2020.103114

In this paper, we explore conditions under which certain elliptic hemivariational inequalities permit equivalent minimization principles. It is shown that for an elliptic variational–hemivariational inequality, under the usual assumptions that guarantee the solution existence and uniqueness, if an additional condition is satisfied, the solution of the variational–hemivariational inequality is also the minimizer of a corresponding energy functional. Then, two variants of the equivalence result are given, that are more convenient to use for applications in contact mechanics and in numerical analysis of the variational–hemivariational inequality. When the convex terms are dropped, the results on the elliptic variational–hemivariational inequalities are reduced to that on “pure” elliptic hemivariational inequalities. Finally, two representative examples from contact mechanics are discussed to illustrate application of the theoretical results.