New assumptions for stability analysis in elliptic optimal control problems
Optimization and Control
2025-11-20 v2
Abstract
This paper is dedicated to the stability analysis of the optimal solutions of a control problem associated with a semilinear elliptic equation. The linear differential operator of the equation is neither monotone nor coercive due to the presence of a convection term. The control appears only linearly, or even it can not appear in an explicit form in the objective functional. Under new assumptions, we prove Lipschitz stability of the optimal controls and associated states with respect to perturbations in the equation and the objective functional as well as with respect to the Tikhonov regularization parameter.
Cite
@article{arxiv.2205.03813,
title = {New assumptions for stability analysis in elliptic optimal control problems},
author = {Eduardo Casas and Alberto Domínguez Corella and Nicolai Jork},
journal= {arXiv preprint arXiv:2205.03813},
year = {2025}
}