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Abstract:

We study the Sobolev trace constant for functions defined in a bounded domain Ω that vanish in the subset A. We find a formula for the first variation of the Sobolev trace with respect to the hole. As a consequence of this formula, we prove that when Ω is a centered ball, the symmetric hole is critical when we consider deformation that preserve volume but is not optimal for some case. © 2010 World Scientific Publishing Company.

Registro:

Documento: Artículo
Título:Optimization problem for extremals of the trace inequality in domains with holes
Autor:Del Pezzo, L.M.
Filiación:Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Pabellón I, Ciudad Universitaria (1428), Buenos Aires, Argentina
Palabras clave:shape derivative; Sobolev trace embedding; Steklov eigenvalues
Año:2010
Volumen:12
Número:4
Página de inicio:569
Página de fin:586
DOI: http://dx.doi.org/10.1142/S0219199710003920
Título revista:Communications in Contemporary Mathematics
Título revista abreviado:Commun. Contemp. Math.
ISSN:02191997
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02191997_v12_n4_p569_DelPezzo

Referencias:

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  • Ferńandez Bonder, J., Groisman, P., Rossi, J.D., Optimization of the first Steklov eigenvalue in domains with holes: A shape derivative approach (2007) Ann. Mat. Pura Appl., 4 (186), pp. 341-358. , 2
  • Ferńandez Bonder, J., Rossi, J.D., A nonlinear eigenvalue problem with indefinite weights related to the Sobolev trace embedding (2002) Publ. Mat., 46 (1), pp. 221-235
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  • Steklov, M.W., Sur les probĺemes fondamentaux en physique math́ematique (1902) Ann. Sci. Ecole Norm. Sup., 19, pp. 445-490
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Citas:

---------- APA ----------
(2010) . Optimization problem for extremals of the trace inequality in domains with holes. Communications in Contemporary Mathematics, 12(4), 569-586.
http://dx.doi.org/10.1142/S0219199710003920
---------- CHICAGO ----------
Del Pezzo, L.M. "Optimization problem for extremals of the trace inequality in domains with holes" . Communications in Contemporary Mathematics 12, no. 4 (2010) : 569-586.
http://dx.doi.org/10.1142/S0219199710003920
---------- MLA ----------
Del Pezzo, L.M. "Optimization problem for extremals of the trace inequality in domains with holes" . Communications in Contemporary Mathematics, vol. 12, no. 4, 2010, pp. 569-586.
http://dx.doi.org/10.1142/S0219199710003920
---------- VANCOUVER ----------
Del Pezzo, L.M. Optimization problem for extremals of the trace inequality in domains with holes. Commun. Contemp. Math. 2010;12(4):569-586.
http://dx.doi.org/10.1142/S0219199710003920