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A Simple Proof of Regularity for $C^{1,\alpha}$ Interface Transmission Problems

A Simple Proof of Regularity for $C^{1,\alpha}$ Interface Transmission Problems
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Year:    2021

Author:    Hongjie Dong

Annals of Applied Mathematics, Vol. 37 (2021), Iss. 1 : pp. 22–30

Abstract

We give an alternative 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 with variable coefficients. This answers a question raised in [1]. Some extensions to $C^{1,\text{Dini}}$ interfaces and to domains with multiple sub-domains are also discussed.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aam.OA-2020-0002

Annals of Applied Mathematics, Vol. 37 (2021), Iss. 1 : pp. 22–30

Published online:    2021-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    9

Keywords:    Transmission problems elliptic systems with variable coefficients $C^{1 \alpha}$ and $C^{1 \text{Dini}}$ interfacial boundaries $C^\alpha$ and Dini coefficients.

Author Details

Hongjie Dong

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