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

doi:10.1524/anly.2009.1046

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

https://doi.org/10.1524/anly.2009.1046

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Abstract

If G ⊂ ℝ² is either a bounded or an exterior domain weak L^q-solutions of Δw = rot^∗p in G, w |_∂G = 0 (p ∈ L^q(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.

Keywords: cosserat spectrum; solenoidal fields

^* Correspondence address: University of Bayreuth, Department of Mathematics, 95440 Bayreuth, Deutschland, christian.simader@uni-bayreuth.de

Published Online: 2009-12-04

Published in Print: 2009-11

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Volume 29 Issue 4

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