Communications in Mathematical Analysis

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

Junichi Aramaki

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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.

Article information

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

Dates
First available in Project Euclid: 20 August 2019

Permanent link to this document
https://projecteuclid.org/euclid.cma/1566266426

Mathematical Reviews number (MathSciNet)
MR3992900

Subjects
Primary: 35A05 35A15: Variational methods 35B65: Smoothness and regularity of solutions 35H30: Quasi-elliptic equations

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

Citation

Aramaki, Junichi. Existence and Regularity of a Weak Solution to the Maxwell-Stokes Type System Containing $p$-curlcurl Equation. Commun. Math. Anal. 22 (2019), no. 1, 34--50. https://projecteuclid.org/euclid.cma/1566266426


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