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The best Sobolev trace constant as limit of the usual Sobolev constant for small strips near the boundary

Arrieta Algarra, José María and Rodríguez Bernal, Aníbal and Rossi, Julio D. (2008) The best Sobolev trace constant as limit of the usual Sobolev constant for small strips near the boundary. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 138 (2). 223-237 . ISSN 0308-2105

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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.


Item Type:Article
Uncontrolled Keywords:Nonlinear boundary conditions, Sobolev trace embedding, Symmetry of extremals
Subjects:Sciences > Mathematics > Differential equations
ID Code:13423
Deposited On:17 Oct 2011 14:59
Last Modified:06 Feb 2014 09:48

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