Exterior domain problems and decomposition of tensor fields in weighted Sobolev spaces

Schwarz, Günter

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URL: http://ub-madoc.bib.uni-mannheim.de/1702
URN: urn:nbn:de:bsz:180-madoc-17025
Document Type: Working paper
Year of publication: 1996
Publication language: English
Institution: School of Business Informatics and Mathematics > Sonstige - Fakultät für Mathematik und Informatik
MADOC publication series: Veröffentlichungen der Fakultät für Mathematik und Informatik > Institut für Mathematik > Mannheimer Manuskripte
Subject: 510 Mathematics
Classification: MSC: 35F15 35J55 58A14 ,
Subject headings (SWD): Tensorfeld , Sobolev-Raum , Dekomposition , Hodge-Zerlegung
Abstract: The Hodge decompOsition is a useful tool for tensor analysis on compact manifolds with boundary. This paper aims at generalising the decomposition to exterior domains G ⊂ IR n. Let L 2a Ω k(G) be the space weighted square integrable differential forms with weight function (1 + |χ|²)a, let d a be the weighted perturbation of the exterior derivative and δ a its adjoint. Then L 2a Ω k(G) splits into the orthogonal sum of the subspaces of the d a-exact forms with vanishing tangential component on the boundary, of δ a-coexact forms with vanishing normal component, and harmonic forms, in the sense of d a λ
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