Advances in Differential Equations

On shape stability of Dirichlet optimal control problems in coefficients for nonlinear elliptic equations

Ciro D'Apice, Umberto De Maio, and Ol'ga P. Kogut

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

In this paper we study a classical Dirichlet optimal control problem for a nonlinear elliptic equation with the coefficients as controls in $L^\infty(\Omega)$. Since such problems have no solutions in general, we make an assumption on the coefficients of the state equation and introduce the class of so-called solenoidal controls. Using the direct method in the calculus of variations, we prove the existence of at least one optimal pair. We also study the stability of the above optimal control problem with respect to the domain perturbation. With this goal we introduce the concept of Mosco-stability for such problems and analyze the variational properties of Mosco-stable problems with respect to different types of domain perturbations.

Article information

Source
Adv. Differential Equations Volume 15, Number 7/8 (2010), 689-720.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355854623

Mathematical Reviews number (MathSciNet)
MR2650585

Zentralblatt MATH identifier
1194.35147

Subjects
Primary: 35B20: Perturbations 35B30: Dependence of solutions on initial and boundary data, parameters [See also 37Cxx] 35J50: Variational methods for elliptic systems 35J65: Nonlinear boundary value problems for linear elliptic equations 47H05: Monotone operators and generalizations 49J20: Optimal control problems involving partial differential equations

Citation

D'Apice, Ciro; De Maio, Umberto; Kogut, Ol'ga P. On shape stability of Dirichlet optimal control problems in coefficients for nonlinear elliptic equations. Adv. Differential Equations 15 (2010), no. 7/8, 689--720. https://projecteuclid.org/euclid.ade/1355854623.


Export citation