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Licensed Unlicensed Requires Authentication Published by Oldenbourg Wissenschaftsverlag December 4, 2009

The Cosserat problem related to the curl and a complete characterization of all solenoidal vector fields vanishing at the boundary in case of space dimension n = 2

  • Christian G. Simader
From the journal


If G ⊂ ℝ2 is either a bounded or an exterior domain weak Lq-solutions of Δw = rotp in G, w |G = 0 (pLq(G) given), are regarded. Because of the simple relation between rot and div in case n = 2 we deduce immediately from the corresponding results for Δv = ∇p in G, v |G = 0, all results for the problem considered above. In addition we derive a complete characterization of all solenoidal vector fields. This depends on topological properties of G.

* Correspondence address: University of Bayreuth, Department of Mathematics, 95440 Bayreuth, Deutschland,

Published Online: 2009-12-04
Published in Print: 2009-11

© by Oldenbourg Wissenschaftsverlag, München, Germany

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