Volume 37, Issue 1
A Simple Proof of Regularity for $C^{1,\alpha}$ Interface Transmission Problems

Hongjie Dong

Ann. Appl. Math., 37 (2021), pp. 22-30.

Published online: 2021-02

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  • 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.

  • AMS Subject Headings

35B65, 35B45, 35J47, 35J25

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COPYRIGHT: © Global Science Press

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@Article{AAM-37-22, author = {Dong , Hongjie}, title = {A Simple Proof of Regularity for $C^{1,\alpha}$ Interface Transmission Problems}, journal = {Annals of Applied Mathematics}, year = {2021}, volume = {37}, number = {1}, pages = {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.

}, issn = {}, doi = {https://doi.org/10.4208/aam.OA-2020-0002}, url = {http://global-sci.org/intro/article_detail/aam/18629.html} }
TY - JOUR T1 - A Simple Proof of Regularity for $C^{1,\alpha}$ Interface Transmission Problems AU - Dong , Hongjie JO - Annals of Applied Mathematics VL - 1 SP - 22 EP - 30 PY - 2021 DA - 2021/02 SN - 37 DO - http://doi.org/10.4208/aam.OA-2020-0002 UR - https://global-sci.org/intro/article_detail/aam/18629.html KW - Transmission problems, elliptic systems with variable coefficients, $C^{1,\alpha}$ and $C^{1,\text{Dini}}$ interfacial boundaries, $C^\alpha$ and Dini coefficients. AB -

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.

Hongjie Dong. (1970). A Simple Proof of Regularity for $C^{1,\alpha}$ Interface Transmission Problems. Annals of Applied Mathematics. 37 (1). 22-30. doi:10.4208/aam.OA-2020-0002
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