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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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Official URL: http://journals.cambridge.org/action/displayJournal?jid=PRM

## 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 |
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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: | 12 Dec 2018 15:07 |

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