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arXiv · 2303.04182

On higher order boundary Harnack and analyticity of free boundaries

Chilin Zhang
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Abstract

We establish a C^1,alpha Schauder estimate of a non-standard degenerate elliptic equation and use it to give another proof of the higher order boundary Harnack inequality. As an application, we obtain the analyticity of the free boundary in the classical obstacle problem based on iterating the boundary Harnack principle.

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Chilin Zhang. 2023-03-07. On higher order boundary Harnack and analyticity of free boundaries. https://doi.org/10.1016/j.na.2023.113471

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