Optimal Control of Semilinear Elliptic Equations in Measure Spaces
Authors:
- Eduardo CasasECEduardo Casas
- Karl KunischKKKarl Kunisch
Open Access
- 1 January 2014
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Control and Optimization
- Vol. 52 (1) , 339-364
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 $L^\infty (\Omega)$ regularity result for solutions of the first order necessary optimality conditions.
Keywords
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