Abstract

In this paper, we provide an alternative approach to establish the solution existence and uniqueness for elliptic variational-hemivariational inequalities. The new approach is based on elementary results from functional analysis, and thus removes the need of the notion of pseudomonotonicity and the dependence on surjectivity results for pseudomonotone operators. This makes the theory of elliptic variational-hemivariational inequalities more accessible to applied mathematicians and engineers. In addition, equivalent minimization principles are further explored for particular elliptic variational-hemivariational inequalities. Representative examples from contact mechanics are discussed to illustrate application of the theoretical results.

摘要

在本文中，我们提供了另一种方法来建立椭圆变分半偏不等式的解存在性和唯一性。该新方法基于功能分析的基本结果，因此消除了对伪单调性概念的需求，也消除了对伪单调算符的异义性结果的依赖。这使得椭圆形变分半不等式理论更适合应用数学家和工程师使用。另外，针对特定的椭圆变分半偏不等式，还进一步探索了等效的最小化原理。讨论了接触力学的典型例子，以说明理论结果的应用。