Optimization problems for elliptic PDEs

TL;DR

This paper studies optimal control problems governed by elliptic PDEs, focusing on different control variables and cost functionals involving both state and control, to improve understanding and solution methods.

Contribution

It introduces a framework for analyzing control problems with various control variables and cost functionals in elliptic PDEs, advancing theoretical understanding.

Findings

Characterization of optimal controls for different control variables

Existence and uniqueness results for the control problems

Development of solution methods for the optimization problems

Abstract

In this paper we consider some optimal control problems governed by elliptic partial differential equations. The solution is the state variable, while the control variable is, depending on the case, the coefficient of the PDE, the potential, the right-hand side. The cost functional is of integral type and involves both the state and control variables.