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

Let u be a vector field on a bounded Lipschitz domain in ℝ 3 , 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 H 1/2 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 L 2 .