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 of Weak Solutions to Maxwell's Equations in a Quasi-static Electromagnetic Field." Methods Appl. Anal. 15 (2) 205 - 222, June 2008.