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July/August 2010 On shape stability of Dirichlet optimal control problems in coefficients for nonlinear elliptic equations
Ciro D'Apice, Umberto De Maio, Ol'ga P. Kogut
Adv. Differential Equations 15(7/8): 689-720 (July/August 2010).

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.

Citation

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Ciro D'Apice. Umberto De Maio. Ol'ga P. Kogut. "On shape stability of Dirichlet optimal control problems in coefficients for nonlinear elliptic equations." Adv. Differential Equations 15 (7/8) 689 - 720, July/August 2010.

Information

Published: July/August 2010
First available in Project Euclid: 18 December 2012

zbMATH: 1194.35147
MathSciNet: MR2650585

Subjects:
Primary: 35B20, 35B30, 35J50, 35J65, 47H05, 49J20

Rights: Copyright © 2010 Khayyam Publishing, Inc.

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Vol.15 • No. 7/8 • July/August 2010
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