Partial regularity of weak solutions to Maxwell’s equations in a quasi-static electromagnetic field. (English) Zbl 1170.35382

Hong, Min-Chun; Tonegawa, Yoshihiro; Yassin, Alzubaidi

Methods Appl. Anal. 15, No. 2, 205-222 (2008).

Summary: 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.

MSC:

35J45	Systems of elliptic equations, general (MSC2000)
35J60	Nonlinear elliptic equations
58E20	Harmonic maps, etc.

Keywords:

partial regularity; elliptic systems; parabolic systems