PARTIAL REGULARITY OF WEAK SOLUTIONS TO MAXWELL'S EQUATIONS IN A QUASI-STATIC ELECTROMAGNETIC FIELD

摘要

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 H_lder 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.