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 - <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>