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Abstract:

In this paper we find estimates for the optimal constant in the critical Sobolev trace inequality S∥u∥Lp*(∂Ω) p≤∥u∥W1,p(Ω) that are independent of Ω. This estimates generalized those of Adimurthi and Yadava (Comm Partial Diff Equ 16(11):1733-1760, 1991) for general p. Here p*: = p(N - 1)/(N - p) is the critical exponent for the immersion and N is the space dimension. Then we apply our results first to prove existence of positive solutions to a nonlinear elliptic problem with a nonlinear boundary condition with critical growth on the boundary, generalizing the results of Fernández Bonder and Rossi (Bull Lond Math Soc 37:119-125, 2005). Finally, we study an optimal design problem with critical exponent. © 2007 Springer-Verlag.

Registro:

Documento: Artículo
Título:Estimates for the Sobolev trace constant with critical exponent and applications
Autor:Fernández Bonder, J.; Saintier, N.
Filiación:Departamento de Matemática, FCEyN UBA, (1428), Buenos Aires, Argentina
Palabras clave:Critical exponents; Optimal design problems; Sobolev trace embedding
Año:2008
Volumen:187
Número:4
Página de inicio:683
Página de fin:704
DOI: http://dx.doi.org/10.1007/s10231-007-0062-1
Título revista:Annali di Matematica Pura ed Applicata
Título revista abreviado:Ann. Mat. Pura Appl.
ISSN:03733114
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03733114_v187_n4_p683_FernandezBonder

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Citas:

---------- APA ----------
Fernández Bonder, J. & Saintier, N. (2008) . Estimates for the Sobolev trace constant with critical exponent and applications. Annali di Matematica Pura ed Applicata, 187(4), 683-704.
http://dx.doi.org/10.1007/s10231-007-0062-1
---------- CHICAGO ----------
Fernández Bonder, J., Saintier, N. "Estimates for the Sobolev trace constant with critical exponent and applications" . Annali di Matematica Pura ed Applicata 187, no. 4 (2008) : 683-704.
http://dx.doi.org/10.1007/s10231-007-0062-1
---------- MLA ----------
Fernández Bonder, J., Saintier, N. "Estimates for the Sobolev trace constant with critical exponent and applications" . Annali di Matematica Pura ed Applicata, vol. 187, no. 4, 2008, pp. 683-704.
http://dx.doi.org/10.1007/s10231-007-0062-1
---------- VANCOUVER ----------
Fernández Bonder, J., Saintier, N. Estimates for the Sobolev trace constant with critical exponent and applications. Ann. Mat. Pura Appl. 2008;187(4):683-704.
http://dx.doi.org/10.1007/s10231-007-0062-1