Publication: The best Sobolev trace constant as limit of the usual Sobolev constant for small strips near the boundary
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Publication Date
2008
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Cambridge University Press
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Abstract
In this paper we prove that the best constant in the Sobolev trace embedding H1() ,! Lq(@) in a bounded smooth domain can be obtained as the limit as " ! 0 of the best constant of the usual Sobolev embedding H1() ,! Lq(!", dx/") where !" = {x 2 : dist(x, @) < "} is a small neighborhood of the boundary. We also analyze symmetry properties of extremals of this last embedding when is a ball.