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Abstract:

In this paper we study the Sobolev embedding theorem for variable exponent spaces with critical exponents. We find conditions on the best constant in order to guaranty the existence of extremals. The proof is based on a suitable refinement of the estimates in the Concentration-Compactness Theorem for variable exponents and an adaptation of a convexity argument due to P.L. Lions, F. Pacella and M. Tricarico. © 2012 Elsevier Inc..

Registro:

Documento: Artículo
Título:On the Sobolev embedding theorem for variable exponent spaces in the critical range
Autor:Fernández Bonder, J.; Saintier, N.; Silva, A.
Filiación:IMAS, CONICET, Argentina
Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Ciudad Universitaria Pabellón I, (1428) Buenos Aires, Argentina
Instituto de Ciencias, Universidad Nacional de General Sarmiento, J.M. Gutierrez 1150, C.P. 1613, Los Polvorines, Pcia de Bs. As., Argentina
Palabras clave:Concentration compactness; Critical exponents; Sobolev embedding; Variable exponents
Año:2012
Volumen:253
Número:5
Página de inicio:1604
Página de fin:1620
DOI: http://dx.doi.org/10.1016/j.jde.2012.05.020
Título revista:Journal of Differential Equations
Título revista abreviado:J. Differ. Equ.
ISSN:00220396
CODEN:JDEQA
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00220396_v253_n5_p1604_FernandezBonder

Referencias:

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Citas:

---------- APA ----------
Fernández Bonder, J., Saintier, N. & Silva, A. (2012) . On the Sobolev embedding theorem for variable exponent spaces in the critical range. Journal of Differential Equations, 253(5), 1604-1620.
http://dx.doi.org/10.1016/j.jde.2012.05.020
---------- CHICAGO ----------
Fernández Bonder, J., Saintier, N., Silva, A. "On the Sobolev embedding theorem for variable exponent spaces in the critical range" . Journal of Differential Equations 253, no. 5 (2012) : 1604-1620.
http://dx.doi.org/10.1016/j.jde.2012.05.020
---------- MLA ----------
Fernández Bonder, J., Saintier, N., Silva, A. "On the Sobolev embedding theorem for variable exponent spaces in the critical range" . Journal of Differential Equations, vol. 253, no. 5, 2012, pp. 1604-1620.
http://dx.doi.org/10.1016/j.jde.2012.05.020
---------- VANCOUVER ----------
Fernández Bonder, J., Saintier, N., Silva, A. On the Sobolev embedding theorem for variable exponent spaces in the critical range. J. Differ. Equ. 2012;253(5):1604-1620.
http://dx.doi.org/10.1016/j.jde.2012.05.020