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If G ⊂ ℝ2 is either a bounded or an exterior domain weak Lq-solutions of Δw = rot∗p in G, w |∂G = 0 (p ∈ Lq(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
Published Online: 2009-12-04
Published in Print: 2009-11
© by Oldenbourg Wissenschaftsverlag, München, Germany