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Abstract:

In this paper we study the problem of minimizing the Sobolev trace Rayleigh quotient ∥u∥W1,p(ω)p/∥u∥Lq(∂ω)p among functions that vanish in a set contained on the boundary ∂ ω of given boundary measure.We prove existence of extremals for this problem, and analyze some particular cases where information about the location of the optimal boundary set can be given. Moreover, we further study the shape derivative of the Sobolev trace constant under regular perturbations of the boundary set. © 2011 Elsevier Inc.

Registro:

Documento: Artículo
Título:Optimal boundary holes for the Sobolev trace constant
Autor:Del Pezzo, L.; Fernández Bonder, J.; Neves, W.
Filiación:IMAS-CONICET and Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Pabellón 1, Ciudad Universitaria (1428), Buenos Aires, Argentina
Instituto de Matematica, Univ. Federal do Rio de Janeiro, C.P. 68530, Cidade Universitária, 21945-970, Rio de Janeiro, Brazil
Palabras clave:P-Laplace operator; Shape optimization; Steklov eigenvalues
Año:2011
Volumen:251
Número:8
Página de inicio:2327
Página de fin:2351
DOI: http://dx.doi.org/10.1016/j.jde.2011.07.006
Título revista:Journal of Differential Equations
Título revista abreviado:J. Differ. Equ.
ISSN:00220396
CODEN:JDEQA
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_00220396_v251_n8_p2327_DelPezzo.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00220396_v251_n8_p2327_DelPezzo

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Citas:

---------- APA ----------
Del Pezzo, L., Fernández Bonder, J. & Neves, W. (2011) . Optimal boundary holes for the Sobolev trace constant. Journal of Differential Equations, 251(8), 2327-2351.
http://dx.doi.org/10.1016/j.jde.2011.07.006
---------- CHICAGO ----------
Del Pezzo, L., Fernández Bonder, J., Neves, W. "Optimal boundary holes for the Sobolev trace constant" . Journal of Differential Equations 251, no. 8 (2011) : 2327-2351.
http://dx.doi.org/10.1016/j.jde.2011.07.006
---------- MLA ----------
Del Pezzo, L., Fernández Bonder, J., Neves, W. "Optimal boundary holes for the Sobolev trace constant" . Journal of Differential Equations, vol. 251, no. 8, 2011, pp. 2327-2351.
http://dx.doi.org/10.1016/j.jde.2011.07.006
---------- VANCOUVER ----------
Del Pezzo, L., Fernández Bonder, J., Neves, W. Optimal boundary holes for the Sobolev trace constant. J. Differ. Equ. 2011;251(8):2327-2351.
http://dx.doi.org/10.1016/j.jde.2011.07.006