Methods and Applications of Analysis
Volume 15 (2008)
Partial Regularity of Weak Solutions to Maxwell's Equations in a Quasi-static Electromagnetic Field
Pages: 205 – 222
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