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, Ω), when Ω is a Lipschitz polyhedron in ℝ3 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 Γ. Such a space is characterized and a basis is furnished.

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