HÖLDER CONTINUITY OF THE SOLUTION MAP TO AN ELLIPTIC OPTIMAL CONTROL PROBLEM WITH MIXED CONSTRAINTS

Abstract

The goal of the paper is to investigate the Hölder continuity of the solution map to a parametric optimal control problem which is governed by elliptic equations with mixed control-state constraints and convex cost functions. By reducing the problem to a programming problem and parametric variational inequality, we get sufficient conditions under which the solution map is Hölder continuous in parameters.