On representation of boundary integrals involving the mean curvature for mean-convex domains

Yoshikazu Giga; Giovanni Pisante

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arXiv · 1303.4281

On representation of boundary integrals involving the mean curvature for mean-convex domains

Yoshikazu Giga·Giovanni Pisante

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Abstract

Given a mean-convex domain $\Omega\subset \R^n$ with boundary of class $C^{2,1}$, we provide a representation formula for a boundary integral of the type \[ \int_{\partial \Omega} f(k(x)) \, d\mathcal{H}^{n-1} \] where $k\geq 0$ is the mean curvature of $\partial \Omega$ and $f$ is non-increasing and sufficiently regular, in terms of volume integrals and defect measure on the ridge set.

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Yoshikazu Giga, Giovanni Pisante. 2013-03-18. On representation of boundary integrals involving the mean curvature for mean-convex domains. https://arxiv.org/abs/1303.4281

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