Existence and approximated results of solutions for a class of nonlocal elliptic variational‐hemivariational inequalities
Yongjian Liu, Zhenhai Liu, Dumitru Motreanu
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.
Topics & Concepts
MathematicsUniquenessRegularization (linguistics)Tikhonov regularizationMathematical analysisApplied mathematicsElliptic operatorPure mathematicsInverse problemComputer scienceArtificial intelligenceContact Mechanics and Variational InequalitiesNonlinear Partial Differential EquationsNumerical methods in engineering