Methods and Applications of Analysis

Volume 15 (2008)

Number 2

Partial Regularity of Weak Solutions to Maxwell's Equations in a Quasi-static Electromagnetic Field

Pages: 205 – 222

DOI: http://dx.doi.org/10.4310/MAA.2008.v15.n2.a7

Authors

Min-Chun Hong

Yoshihiro Tonegawa

Alzubaidi Yassin

Abstract

We study Maxwell's equations in a quasi-static electromagnetic field, where the electrical conductivity of the material depends on the temperature. By establishing the reverse Hölder inequality, we prove partial regularity of weak solutions to the non-linear elliptic system and the non-linear parabolic system in a quasi-static electromagnetic field.

Keywords

Partial regularity; elliptic systems; parabolic systems

2010 Mathematics Subject Classification

35J60, 58E20

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