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

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.
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