An epiperimetric inequality for odd frequencies in the thin obstacle problem

Matteo Carducci; Bozhidar Velichkov

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arXiv · 2409.12110

An epiperimetric inequality for odd frequencies in the thin obstacle problem

Matteo Carducci·Bozhidar Velichkov

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Abstract

We prove for the first time an epiperimetric inequality for the thin obstacle Weiss' energy with odd frequencies and we apply it to solutions to the thin obstacle problem with general $C^{k,\gamma}$. In particular, we obtain the rate of convergence of the blow-up sequences at points of odd frequencies and the regularity of the strata of the corresponding contact set. We also recover the frequency gap for odd frequencies obtained by Savin and Yu.

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Matteo Carducci, Bozhidar Velichkov. 2024-09-18. An epiperimetric inequality for odd frequencies in the thin obstacle problem. https://arxiv.org/abs/2409.12110

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