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Estimating ∇ u in terms of div u , curl u , either (ν, u ) or ν× u and the topology
Author(s) -
Bolik Jürgen,
von Wahl Wolf
Publication year - 1997
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(199706)20:9<737::aid-mma863>3.0.co;2-i
Subject(s) - mathematics , cohomology , bounded function , boundary (topology) , vector field , boundary value problem , curl (programming language) , a priori and a posteriori , pure mathematics , boundary values , field (mathematics) , discrete mathematics , mathematical analysis , geometry , philosophy , epistemology , computer science , programming language
In the present paper we prove C α ‐estimates for ∇ u using components of boundary values of u , div u , curl u and quantities given by components of boundary values of u as well as boundary values of elements belonging to de Rhams cohomology modules. The vector field u is defined on a bounded set G ¯⊂ℝ 3 , meanwhile the cohomology group will be defined with regard to ℝ 3 − G . Our inequalities turn out to be a priori estimates concerning well‐known boundary value problems for vector fields. © 1997 by B. G. Teubner Stuttgart–John Wiley & Sons Ltd.