Optimization problems for the energy integral of p-Laplace equations

Antonio Greco; Giovanni Porru

doi:10.3934/proc.2013.2013.301

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2013, Volume 2013: 301-310. Doi: 10.3934/proc.2013.2013.301 open access

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Optimization problems for the energy integral of p-Laplace equations

Antonio Greco^1, and
Giovanni Porru^1,

1.
Department of Mathematics and Informatics, Via Ospedale 72, 09124 Cagliari

Received: July 31, 2012

Revised: October 31, 2012

Published: October 2013

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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 $\alpha$.

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Mathematics Subject Classification: Primary: 35J20, 35J92; Secondary: 49K20, 52A40.

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