On the use of elliptic regularity theory for the numerical solution of variational problems

Abstract

In this article we show the crucial role of elliptic regularity theory for the development of efficient numerical methods for the solution of some variational problems. Here we focus to a class of elliptic multiobjective optimal control problems that can be formulated as jointly convex generalized Nash equilibrium problems and to nonsmooth boundary value problems that stem from contact mechanics leading to elliptic variational inequalities.