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Optimization problems for the energy integral of p-Laplace equations

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  • 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 $D\subset\Omega$ is a variable subset 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 $\alpha$.
    Mathematics Subject Classification: Primary: 35J20, 35J92; Secondary: 49K20, 52A40.


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