We study maximization and minimization problems for the energy integral of a sub-linear p-Laplace equation in a domain Omega, with weight chi_D, where D is a variable subset of Omega with a fixed measure alpha. We prove Lipschitz continuity for the energy integral of a maximizer and differentiability for the energy integral of the minimizer with respect to alpha.
Optimization problems for the energy integral of p-Laplace equations
GRECO, ANTONIO;
2013-01-01
Abstract
We study maximization and minimization problems for the energy integral of a sub-linear p-Laplace equation in a domain Omega, with weight chi_D, where D is a variable subset of Omega with a fixed measure alpha. We prove Lipschitz continuity for the energy integral of a maximizer and differentiability for the energy integral of the minimizer with respect to alpha.
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