Existence and $W^{1,p}$ estimates of certain Maxwell type equations in Reifenberg domains

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.