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Abstract:

We study the dependence on the subset A ⊂ Ω of the Sobolev trace constant for functions defined in a bounded domain Ω that vanish in the subset A. First we find that there exists an optimal subset that makes the trace constant smaller among all the subsets with prescribed and positive Lebesgue measure. In the case that Ω is a ball we prove that there exists an optimal hole that is spherically symmetric. In the case p = 2 we prove that every optimal hole is spherically symmetric. Then, we study the behavior of the best constant when the hole is allowed to have zero Lebesgue measure. We show that this constant depends continuously on the subset and we discuss when it is equal to the Sobolev trace constant without the vanishing restriction. © 2005 Elsevier SAS. All rights reserved.

Registro:

Documento: Artículo
Título:On the best Sobolev trace constant and extremals in domains with holes
Autor:Fernández Bonder, J.; Rossi, J.D.; Wolanski, N.
Filiación:Departamento de Matemática, FCEyN UBA, 1428 Buenos Aires, Argentina
Consejo Superior de Investigaciones Científicas (CSIC), Serrano 117, Madrid, Spain
Palabras clave:Eigenvalue optimization problems; p-capacity; p-Laplacian; Sobolev trace constant
Año:2006
Volumen:130
Número:7
Página de inicio:565
Página de fin:579
DOI: http://dx.doi.org/10.1016/j.bulsci.2005.10.005
Título revista:Bulletin des Sciences Mathematiques
Título revista abreviado:Bull. Sci. Math.
ISSN:00074497
CODEN:BSMQA
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_00074497_v130_n7_p565_FernandezBonder.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00074497_v130_n7_p565_FernandezBonder

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Citas:

---------- APA ----------
Fernández Bonder, J., Rossi, J.D. & Wolanski, N. (2006) . On the best Sobolev trace constant and extremals in domains with holes. Bulletin des Sciences Mathematiques, 130(7), 565-579.
http://dx.doi.org/10.1016/j.bulsci.2005.10.005
---------- CHICAGO ----------
Fernández Bonder, J., Rossi, J.D., Wolanski, N. "On the best Sobolev trace constant and extremals in domains with holes" . Bulletin des Sciences Mathematiques 130, no. 7 (2006) : 565-579.
http://dx.doi.org/10.1016/j.bulsci.2005.10.005
---------- MLA ----------
Fernández Bonder, J., Rossi, J.D., Wolanski, N. "On the best Sobolev trace constant and extremals in domains with holes" . Bulletin des Sciences Mathematiques, vol. 130, no. 7, 2006, pp. 565-579.
http://dx.doi.org/10.1016/j.bulsci.2005.10.005
---------- VANCOUVER ----------
Fernández Bonder, J., Rossi, J.D., Wolanski, N. On the best Sobolev trace constant and extremals in domains with holes. Bull. Sci. Math. 2006;130(7):565-579.
http://dx.doi.org/10.1016/j.bulsci.2005.10.005