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The existence of solutions of a general boundary value problem for the divergence

✍ Scribed by G. Schwarz

Publisher
John Wiley and Sons
Year
1994
Tongue
English
Weight
539 KB
Volume
17
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

This paper is concerned with the question of necessary and sufficient conditions to find a vector field V∈ Ξ“(TM) solving the equation div V = Ξ¦ under inhomogeneous boundary conditions V|~βˆ‚M~ = Z|~βˆ‚M~ with Z∈ Ξ“ (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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