Optimal control of semilinear elliptic equations with pointwise constraints on the gradient of the state
type: Item
instance of: scholarly article
title: Optimal control of semilinear elliptic equations with pointwise constraints on the gradient of the state
zbMATH Open document ID: 0761.49010
DOI: 10.1007/BF01182597
author: Eduardo Casas
author: Luis Alberto Fernández
published in: Applied Mathematics and Optimization
publication date: 1993-04-01T00:00:00Z
review text: The authors consider an optimal control problem of semilinear elliptic equations subject to control constraints and pointwise constraints on the gradient of the state. The control is distributed and assumed to belong to \(L^ r(\Omega)\) for some \(r>n\), thus allowing not to choose the control space among Sobolev spaces. So the main results obtained in the paper are: optimality conditions with more general state constraints and simpler Lagrange multiplier than in previous papers; regularity results; a detailed study of the adjoint state equation.
reviewed by: Vladimír B. Kamen
Mathematics Subject Classification ID: 49K20
Mathematics Subject Classification ID: 49J20
zbMATH DE Number: 147399
zbMATH Keywords: state constraints
zbMATH Keywords: distributed control
zbMATH Keywords: semilinear elliptic equations
zbMATH Keywords: optimality conditions
zbMATH Keywords: Lagrange multiplier
zbMATH Keywords: regularity results
zbMATH Keywords: adjoint state equation
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 147399