Hodge decompositions on the boundary of nonsmooth domains: The multi-connected case

This paper concerns the characterization of tangential traces for the space H(curl, Omega), when Omega is a Lipschitz polyhedron in R-3 under general topology assumptions. Suitable spaces of tangential vector fields are introduced and characterized. Hodge decompositions are provided and they involve the first cohomology space of the boundary Gamma. Such a space is characterized and a basis is furnished.