A remark on the regularity of solutions of Maxwell's equations on Lipschitz domains

Abstract

AbstractLet u be a vector field on a bounded Lipschitz domain in ℝ3, and let u together with its divergence and curl be square integrable. If either the normal or the tangential component of u is square integrable over the boundary, then u belongs to the Sobolev space H1/2 on the domain. This result gives a simple explanation for known results on the compact embedding of the space of solutions of Maxwell's equations on Lipschitz domains into L2.