An epiperimetric inequality for odd frequencies in the thin obstacle problem

2024/09/18 by Matteo Carducci, Carducci, Matteo, Bozhidar Velichkov +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2409.12110

openalex publication_date 2024/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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,γ. 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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