On traces for functional spaces related to Maxwell's equations Part II: Hodge decompositions on the boundary of Lipschitz polyhedra and applications

Hedge decompositions of tangential vector fields defined on piecewise regul ar manifolds are provided. The first step is the study of L-2 tangential fi elds and then the attention is focused on some particular Sobolev spaces of order - 1/2. In order to reach this goal, it is required to properly defin e the first order differential operators and to investigate their propertie s. When the manifold Gamma is the boundary of a polyhedron Omega, these spa ces are important in the analysis of tangential trace mappings for vector f ields in H(curl, Omega) on the whole boundary or on a part of it. By means of,these Hedge decompositions, one can then provide a complete characteriza tion of these trace mappings: general extension theorems, from the boundary , or from a part of it, to the inside; definition of suitable dualities and validity of integration by parts formulae. Copyright (C) 2001 John Wiley & Sons, Ltd.