## Tokyo Journal of Mathematics

- Tokyo J. Math.
- Volume 39, Number 1 (2016), 83-100.

### Interface Regularity of the Solutions to Maxwell Systems on Riemannian Manifolds

Makoto KANOU, Tomohiko SATO, and Kazuo WATANABE

#### Abstract

In this paper we study the interface regularity of the solutions to the differential systems defined by differential forms (for example, stationary Maxwell systems) on $N(\geq 3)$-dimensional Riemannian manifolds. Our results are natural extensions of the results of \textit{Interface regularity of the solutions for the rotation free and the divergence free systems} and \textit{Interface vanishing for solutions to Maxwell and Stokes systems}.

#### Article information

**Source**

Tokyo J. Math., Volume 39, Number 1 (2016), 83-100.

**Dates**

First available in Project Euclid: 30 March 2016

**Permanent link to this document**

https://projecteuclid.org/euclid.tjm/1459367259

**Digital Object Identifier**

doi:10.3836/tjm/1459367259

**Mathematical Reviews number (MathSciNet)**

MR3543133

**Zentralblatt MATH identifier**

1350.35052

**Subjects**

Primary: 35B65: Smoothness and regularity of solutions

Secondary: 35Q60: PDEs in connection with optics and electromagnetic theory 35Q61: Maxwell equations 35R01: Partial differential equations on manifolds [See also 32Wxx, 53Cxx, 58Jxx] 76N10: Existence, uniqueness, and regularity theory [See also 35L60, 35L65, 35Q30] 76W05: Magnetohydrodynamics and electrohydrodynamics

#### Citation

KANOU, Makoto; SATO, Tomohiko; WATANABE, Kazuo. Interface Regularity of the Solutions to Maxwell Systems on Riemannian Manifolds. Tokyo J. Math. 39 (2016), no. 1, 83--100. doi:10.3836/tjm/1459367259. https://projecteuclid.org/euclid.tjm/1459367259