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
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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
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Palabras clave: | Concentration compactness; Critical exponents; Sobolev embedding; Variable exponents |
Año: | 2012
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Volumen: | 253
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Número: | 5
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Página de inicio: | 1604
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Página de fin: | 1620
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DOI: |
http://dx.doi.org/10.1016/j.jde.2012.05.020 |
Título revista: | Journal of Differential Equations
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Título revista abreviado: | J. Differ. Equ.
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ISSN: | 00220396
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CODEN: | JDEQA
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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