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Quasi‐Lipschitz condition in potential theory
Author(s) -
Rautmann Reimund,
Solonnikov Vsevolod
Publication year - 2005
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310255
Subject(s) - lipschitz continuity , mathematics , infimum and supremum , bounded function , vorticity , norm (philosophy) , domain (mathematical analysis) , lipschitz domain , pure mathematics , mathematical analysis , vortex , physics , political science , law , thermodynamics
The velocity $ \vec v $ of an incompressible flow in a bounded three‐dimensional domain is represented by its vorticity $ \vec j $ with the help of an apparently new representation formula. Using this formula we prove a quasi‐Lipschitz estimate for $ \vec v $ in dependence of the supremum norm of $ \vec j $ . Our quasi‐Lipschitz bound extends to the case where $ \vec v $ is represented by any continuous $ \vec j $ ≠ rot $ \vec v $