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arXiv · 2404.04060

The Hadamard variational formula for Riesz capacity and its applications

Lu Zhang
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Abstract

In this paper, our focus lies on a fundamental geometric invariant known as Riesz capacity, which holds an essential position in potential theory. We establish the Hadamard variational formula for Riesz capacity of convex bodies. As a meaningful application, we derive a Serrin-type symmetry result for an overdetermined problem.

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Lu Zhang. 2024-04-05. The Hadamard variational formula for Riesz capacity and its applications. https://arxiv.org/abs/2404.04060

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