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arXiv · 2305.03498

Characterization of the subdifferential and minimizers for the anisotropic p-capacity

Esther Cabezas-Rivas·Salvador Moll·Marcos Solera
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Abstract

We obtain existence of minimizers for the $p$-capacity functional defined with respect to a centrally symmetric anisotropy for $1 < p<\infty$, including the case of a crystalline norm in $\mathbb R^N$. The result is obtained by a characterization of the corresponding subdifferential and it applies for unbounded domains of the form $\mathbb R^N \setminus \overline{\Omega}$ under mild regularity assumptions (Lipschitz-continuous boundary) and no convexity requirements on the bounded domain $\Omega$. If we further assume an interior ball condition (where the Wulff shape plays the role of a ball), then any minimizer is shown to be Lipschitz continuous.

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Esther Cabezas-Rivas, Salvador Moll, Marcos Solera. 2023-05-05. Characterization of the subdifferential and minimizers for the anisotropic p-capacity. https://arxiv.org/abs/2305.03498

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