A simple proof of regularity for $C^{1,\alpha}$ interface transmission problems

Hongjie Dong

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arXiv · 2004.09365

A simple proof of regularity for $C^{1,\alpha}$ interface transmission problems

Hongjie Dong

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Abstract

We give a simple proof of a recent result in [1] by Caffarelli, Soria-Carro, and Stinga about the $C^{1,\alpha}$ regularity of weak solutions to transmission problems with $C^{1,\alpha}$ interfaces. Our proof does not use the mean value property or the maximum principle, and also works for more general elliptic systems. Some extensions to $C^{1,\text{Dini}}$ interfaces and to domains with multiple sub-domains are also discussed.

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Hongjie Dong. 2020-04-20. A simple proof of regularity for $C^{1,\alpha}$ interface transmission problems. https://arxiv.org/abs/2004.09365

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