Symmetrization and optimal control for elliptic equations
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- by Charles Voas and Daniel Yaniro PDF
- Proc. Amer. Math. Soc. 99 (1987), 509-514 Request permission
Abstract:
We consider an optimal control problem where $u(x)$ satisfies $- \operatorname {div}(H(x)\nabla u) = 1$ in $\Omega$ and $H(x)$ is a control. We introduce the functional ${J_\Omega }(H) = {|\Omega |^{ - 1}}\int \limits _\Omega {u(x)} dx$ and show using a symmetrization argument that if the distribution function of $H$ is fixed, then ${J_\Omega }(H)$ is largest when $\Omega$ is a ball and $H$ is radial and decreasing on radii.References
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Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 99 (1987), 509-514
- MSC: Primary 49B22; Secondary 35B37, 35J20
- DOI: https://doi.org/10.1090/S0002-9939-1987-0875390-X
- MathSciNet review: 875390