We study tangential vector fields on the boundary of a bounded Lipschitz domain Omega in R-3. Our attention is focused on the definition of suitable Hilbert spaces corresponding to fractional Sobolev regularities and also on the construction of tangential differential operators on the non-smooth manifold. The theory is applied to the characterization of tangential traces for the space H(curl, Omega). Hodge decompositions are provided for the corresponding trace spaces, and an integration by parts formula is proved.
On traces for H(curl, Omega) in Lipschitz domains
Buffa A;
2002
Abstract
We study tangential vector fields on the boundary of a bounded Lipschitz domain Omega in R-3. Our attention is focused on the definition of suitable Hilbert spaces corresponding to fractional Sobolev regularities and also on the construction of tangential differential operators on the non-smooth manifold. The theory is applied to the characterization of tangential traces for the space H(curl, Omega). Hodge decompositions are provided for the corresponding trace spaces, and an integration by parts formula is proved.File in questo prodotto:
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