@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 = {<p style="text-align: justify;">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.</p>},
issn = {},
doi = {https://doi.org/10.4208/aam.OA-2020-0002},
url = {http://global-sci.org/intro/article_detail/aam/18629.html}
}