On traces for H(curl,Ω) in Lipschitz domains
By Annalisa Buffa, Martin Costabel, Dongwoo Sheen. 2002
428 citations recorded by the source corpus.
Abstract We study tangential vector fields on the boundary of a bounded Lipschitz domain Ω 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 ,Ω) . Hodge decompositions are provided for the corresponding trace spaces, and an integration by parts formula is proved.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/c9c9000b5da16e3b66566f6c0950371bb151ea2a
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In Applied Mathematics
In Computational Theory and Mathematics
In Mathematical Physics
Citations in the corpus
- Galerkin Boundary Element Methods for Electromagnetic Scattering (2003, methodology): “The issue of traces of H(curl; ) for general Lipschitz-domains was finally settled jointly by one of the authors, M. Costabel and D. Sheen in [ 20 ].”
- Surface Plasmon Resonance of Nanoparticles and Applications in Imaging (2014, neutral): “d with the norms kφk TH(div,∂D) = kφkL2(∂D) +k∇∂D · φkL2(∂D), kφk TH(curl,∂D) = kφkL2(∂D) +k∇∂D ·(φ×ν)kL2(∂D). We define the vectorial curl for ϕ∈ H1(∂D) by curl∂Dϕ= −ν×∇∂Dϕ. The following result from [24] will be useful. Proposition 4.1. The following Helmholtz decomposition holds: L2 T(∂D) = ∇ ∂D(H”