The Existence of Solutions of a General Boundary Value Problem for the Divergence


Schwarz, Günter


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URL: https://ub-madoc.bib.uni-mannheim.de/1676
URN: urn:nbn:de:bsz:180-madoc-16760
Document Type: Working paper
Year of publication: 1992
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
Subject headings (SWD): Divergenz <Vektoranalysis> , Riemannscher Raum , Hodge-Theorie , Differentialform
Abstract: This paper is concerned with the question of necessary and sufficient conditions to find a vector field V ∈ Γ(T M) solving the equation divV = Φ under inhomogenous boundary conditions V|ϑM = Z|∈ Γ(TM). An existence and regularity result is given for an arbitrary Riemannian manifold with boundary, M. The proof is based on the Hodge theory of differential forms.
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Schwarz, Günter (1992) The Existence of Solutions of a General Boundary Value Problem for the Divergence. Open Access [Working paper]
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