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



Min-Chun Hong

Yoshihiro Tonegawa

Alzubaidi Yassin


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.


Partial regularity; elliptic systems; parabolic systems

2010 Mathematics Subject Classification

35J60, 58E20

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