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January/February 2021 Existence and $W^{1,p}$ estimates of certain Maxwell type equations in Reifenberg domains
Zhihong Chen, Dongsheng Li
Adv. Differential Equations 26(1/2): 83-106 (January/February 2021).

Abstract

In this paper, we consider a system related to Maxwell's equations, which has different structure with general elliptic systems. The existence of the weak solution is obtained in Reifenberg domain. By assuming that the coefficient matrix belongs to BMO with small seminorm, we establish the $W^{1,p}$ regularity in Reifenberg domain. The main analytical tools are the modified Vitali covering lemma, the maximal function technique and the compactness method.

Citation

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Zhihong Chen. Dongsheng Li. "Existence and $W^{1,p}$ estimates of certain Maxwell type equations in Reifenberg domains." Adv. Differential Equations 26 (1/2) 83 - 106, January/February 2021.

Information

Published: January/February 2021
First available in Project Euclid: 12 January 2021

MathSciNet: MR4198543

Subjects:
Primary: 35B65, 35J70, 35Q61

Rights: Copyright © 2021 Khayyam Publishing, Inc.

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Vol.26 • No. 1/2 • January/February 2021
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