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Optimization problems for the energy integral of p-Laplace equations

Pages: 301 - 310, Issue special, November 2013

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Antonio Greco - Department of Mathematics and Informatics, Via Ospedale 72, 09124 Cagliari, Italy (email)
Giovanni Porru - Department of Mathematics and Informatics, Via Ospedale 72, 09124 Cagliari, Italy (email)

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 $D\subset\Omega$ 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 $\alpha$.

Keywords:  Energy integral, rearrangements, optimization, regularity.
Mathematics Subject Classification:  Primary: 35J20, 35J92; Secondary: 49K20, 52A40.

Received: August 2012;      Revised: November 2012;      Published: November 2013.

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