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

Commun. Math. Anal.
Volume 22, Number 1 (2019), 34 - 50

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

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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.