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Optimal control of semilinear elliptic equations with pointwise constraints on the gradient of the state

Optimal control of semilinear elliptic equations with pointwise constraints on the gradient of... In this paper we are concerned with optimal control problems governed by an elliptic semilinear equation, the control being distributed in Ω. The existence of constraints on the control as well as pointwise constraints on the gradient of the state is assumed. A convenient choice of the control space permits us to derive the optimality conditions and study the adjoint state equation, which has derivatives of measures as data. In order to carry out this study, we prove a trace theorem and state Green's formula by using the transposition method. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Optimal control of semilinear elliptic equations with pointwise constraints on the gradient of the state

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References (20)

Publisher
Springer Journals
Copyright
Copyright © 1993 by Springer-Verlag New York Inc.
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
ISSN
0095-4616
eISSN
1432-0606
DOI
10.1007/BF01182597
Publisher site
See Article on Publisher Site

Abstract

In this paper we are concerned with optimal control problems governed by an elliptic semilinear equation, the control being distributed in Ω. The existence of constraints on the control as well as pointwise constraints on the gradient of the state is assumed. A convenient choice of the control space permits us to derive the optimality conditions and study the adjoint state equation, which has derivatives of measures as data. In order to carry out this study, we prove a trace theorem and state Green's formula by using the transposition method.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Feb 2, 2005

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