Published Paper

Inserted: 19 sep 2024
Last Updated: 15 jul 2025

Journal: J. Funct. Anal.
Year: 2024
Doi: 10.1016/j.jfa.2025.111115

Abstract:

We prove 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 $C^{k,\gamma}$ obstacle. 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.