W1,p Regularity of Weak Solutions to Maxwell’s Equations

Abstract EN

In this paper, we study the steady-state Maxwell’s equations.

The weak solution defined in weak formulation is considered, and the global existence is obtained in general bounded open domain.

The interior W1,p2≤p<∞ estimates of the weak solution are obtained, where the coefficient matrix is assumed to be BMO with small seminorm.

The main analytical tools are the Vitali covering lemma, the maximal function technique, and the compactness method.

We also consider the time-harmonic Maxwell’s equations and obtain the interior W1,p estimates.