An epiperimetric inequality for odd frequencies in the thin obstacle problem

Matteo Carducci, Bozhidar Velichkov
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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.
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薄障碍物问题中奇数频率的外延不等式
我们证明了具有奇数频率的薄障碍韦斯能量的外延不等式,并将其应用于具有一般$C^{k,\gamma}$障碍的薄障碍问题的解。特别是,我们得到了奇数频率点上炸开序列的收敛率以及相应接触集的层的规则性。我们还恢复了由 Savin 和 Yu.
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