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2019 Existence and Regularity of a Weak Solution to the Maxwell-Stokes Type System Containing $p$-curlcurl Equation
Junichi Aramaki
Commun. Math. Anal. 22(1): 34-50 (2019).

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.

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Junichi Aramaki. "Existence and Regularity of a Weak Solution to the Maxwell-Stokes Type System Containing $p$-curlcurl Equation." Commun. Math. Anal. 22 (1) 34 - 50, 2019.

Information

Published: 2019
First available in Project Euclid: 20 August 2019

zbMATH: 07161354
MathSciNet: MR3992900

Subjects:
Primary: 35A05 , 35A15 , 35B65 , 35H30

Keywords: $p$-curlcurl operator , Maxwell-Stokes type system , multiply-connected domain with holes , regularity , Weak solution

Rights: Copyright © 2019 Mathematical Research Publishers

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Vol.22 • No. 1 • 2019
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