In this paper, we introduce a new Tykhonov-type well-posedness concept for elliptic hemivariational inequalities, governed by an approximating function h. We characterize the well-posedness in terms of the metric properties of the family of approximating sets, under various assumptions on h. Then, we use the well-posedness properties in order to obtain convergence results of the solution with respect to the data. The proofs are based on arguments of monotonicity combined with the properties of the Clarke directional derivative. Our results provide mathematical tools in the study of a large number of static problems in Contact Mechanics. To provide an example, we consider a mathematical model which describes the equilibrium of a rod–spring system with unilateral constraints. We prove the unique weak solvability of the model, and then we illustrate our abstract convergence results in the study of this contact problem and provide the corresponding mechanical interpretations.

在本文中，我们为椭圆半变不等式引入了一个新的Tykhonov型适定性概念，该概念由一个近似函数h决定。在关于h的各种假设下，我们根据近似集族的度量属性来描述适定性。然后，我们使用适定性属性以获得关于数据的解的收敛结果。证明是基于单调性的论点以及Clarke定向导数的性质。我们的结果为研究接触力学中的大量静态问题提供了数学工具。为了提供一个例子，我们考虑一个数学模型，该模型描述了具有单边约束的杆-弹簧系统的平衡。我们证明了该模型独特的弱可解性，然后在研究该接触问题时说明了我们的抽象收敛结果，并提供了相应的力学解释。