Optimal control of semilinear elliptic equations in measure spaces
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Identificadores
URI: http://hdl.handle.net/10902/4583DOI: 10.1137/13092188X
ISSN: 1095-7138
ISSN: 0363-0129
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2014Derechos
© 2014 Society for Industrial and Applied Mathematics
Publicado en
Siam Journal on Control and Optimization, 2014, 52(1), 339-364
Publisher
Society for Industrial and Applied Mathematics
Palabras clave
Measure controls
Optimal control
Sparsity
Semilinear elliptic equation
First and second order optimality conditions
Stability analysis
Abstract:
Optimal control problems in measure spaces governed by semilinear elliptic equations are considered. First order optimality conditions are derived and structural properties of their solutions, in particular sparsity, are discussed. Necessary and sufficient second order optimality conditions are obtained as well. On the basis of the sufficient conditions, stability of the solutions is analyzed. Highly nonlinear terms can be incorporated by utilizing an L∞(Ω) regularity result for solutions of the first order necessary optimality conditions.
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