Existence and Regularity of a Weak Solution to the Maxwell-Stokes Type System Containing $p$-curlcurl Equation

Abstract

We consider the existence and regularity of a weak solution to the Maxwell-Stokes type system containing a $p$-curlcurl equation in a multiply-connected domain with holes. In this paper, we shows that the compatibility condition is necessary and sufficient for the existence of a weak solution to the Maxwell-Stokes type system, and that the unique solution has the $C^{1,\beta}$-regularity. The $C^{1,\beta}$-regularity is optimal.