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On the Hölder Continuity of Solutions of a Certain System Related to Maxwell's Equations

We study the system curl (a(x) curl u )=0 , divu = 0 with a bounded measurable coefficient a(x). The main result of this paper is the Holder continuity of weak solutions of the system above. As an application, we prove the Cα regularity of weak solutions of the Maxwell's equations in a quasi-stationary electromagnetic field.