On traces for functional spaces related to Maxwell's equations Part I: An integration by parts formula in Lipschitz polyhedra

Abstract

The aim of this paper is to study the tangential trace and tangential components of fields which belong to the space H(curl, Ω), when Ω is a polyhedron with Lipschitz continuous boundary. The appropriate functional setting is developed in order to suitably define these traces on the whole boundary and on a part of it (for partially vanishing fields and general ones.) In both cases it is possible to define ad hoc dualities among tangential trace and tangential components. In addition, the validity of two related integration by parts formulae is provided. Copyright © 2001 John Wiley & Sons, Ltd.