Methods and Applications of Analysis

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

Min-Chun Hong, Yoshihiro Tonegawa, and Alzubaidi Yassin

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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.

Article information

Source
Methods Appl. Anal., Volume 15, Number 2 (2008), 205-222.

Dates
First available in Project Euclid: 1 September 2009

Permanent link to this document
https://projecteuclid.org/euclid.maa/1251827665

Mathematical Reviews number (MathSciNet)
MR2481680

Zentralblatt MATH identifier
1170.35382

Subjects
Primary: 35J45 35J60: Nonlinear elliptic equations 58E20: Harmonic maps [See also 53C43], etc.

Keywords
Partial regularity elliptic systems parabolic systems

Citation

Hong, Min-Chun; Tonegawa, Yoshihiro; Yassin, Alzubaidi. Partial Regularity of Weak Solutions to Maxwell's Equations in a Quasi-static Electromagnetic Field. Methods Appl. Anal. 15 (2008), no. 2, 205--222. https://projecteuclid.org/euclid.maa/1251827665


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