We prove an inequality for the H"{o}lder continuity of a continuously differentiable function in a bounded open Lipschitz set, which generalizes an inequality of Carlo Miranda in a bounded open hypograph of a function of class $C^{1,alpha}$ for some $alphain ]0,1]$ and which enables to simplify a proof of a result of Carlo Miranda for layer potentials with moment in a Schauder space.
An Inequality for Hölder Continuous Functions Generalizing a Result of Carlo Miranda
M. Lanza de Cristoforis
2020
Abstract
We prove an inequality for the H"{o}lder continuity of a continuously differentiable function in a bounded open Lipschitz set, which generalizes an inequality of Carlo Miranda in a bounded open hypograph of a function of class $C^{1,alpha}$ for some $alphain ]0,1]$ and which enables to simplify a proof of a result of Carlo Miranda for layer potentials with moment in a Schauder space.
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