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Density lower bound estimate for local minimizer of free interface problem with volume constraint

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Abstract

We prove a density lower bound for some functionals involving bulk and interfacial energies. The bulk energies are convex functions with p-power growth not subjected to any further structure conditions. The interface \(\partial E\) is the boundary of a set \(E\subset \Omega \) such that \(|E|=d\) is prescribed. Then we get \(\mathcal {H}^{n-1}((\partial E{\setminus }\partial E^*)\cup \Omega )=0\).

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  1. Dipartimento di Matematica, Via Giovanni Paolo II, 132, 84084, Fisciano, SA, Italy

    Luca Esposito

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  1. Luca Esposito
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Correspondence to Luca Esposito.

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Esposito, L. Density lower bound estimate for local minimizer of free interface problem with volume constraint. Ricerche mat 68, 359–373 (2019). https://doi.org/10.1007/s11587-018-0407-7

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  • DOI: https://doi.org/10.1007/s11587-018-0407-7

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