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Abstract:

In this paper we provide a proof of the Sobolev–Poincaré inequality for variable exponent spaces by means of mass transportation methods, in the spirit of Cordero-Erausquin et al. (Adv Math 182(2):307–332, 2004). The importance of this approach is that the method is flexible enough to deal with different inequalities. As an application, we also deduce the Sobolev-trace inequality improving the result of Fan (J Math Anal Appl 339(2):1395–1412, 2008) by obtaining an explicit dependence of the exponent in the constant. © 2016, Springer-Verlag Berlin Heidelberg.

Registro:

Documento: Artículo
Título:A mass transportation approach for Sobolev inequalities in variable exponent spaces
Autor:Borthagaray, J.P.; Fernández Bonder, J.; Silva, A.
Filiación:IMAS - CONICET and Departamento de Matemática, FCEyN - Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, Buenos Aires, 1428, Argentina
IMASL - CONICET and Departamento de Matemática, Universidad Nacional de San Luis, San Luis, 5700, Argentina
Palabras clave:46E35; 49J40
Año:2016
Volumen:151
Número:1-2
Página de inicio:133
Página de fin:146
DOI: http://dx.doi.org/10.1007/s00229-016-0830-6
Título revista:Manuscripta Mathematica
Título revista abreviado:Manuscr. Math.
ISSN:00252611
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00252611_v151_n1-2_p133_Borthagaray

Referencias:

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  • Cordero-Erausquin, D., Nazaret, B., Villani, C., A mass-transportation approach to sharp Sobolev and Gagliardo–Nirenberg inequalities (2004) Adv. Math., 182 (2), pp. 307-332
  • Diening, L., Riesz potential and Sobolev embeddings on generalized Lebesgue and Sobolev spaces Lp ( · ) and Wk , p ( · ) (2004) Math. Nachr., 268, pp. 31-43
  • Diening, L., Harjulehto, P., Hästö, P., Růžička, M., (2011) Lebesgue and Sobolev Spaces with Variable Exponents, Volume 2017 of Lecture Notes in Mathematics, , Springer, Heidelberg
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  • Edmunds, D.E., Rákosník, J., Sobolev embeddings with variable exponent, II (2002) Math. Nachr., 246-247, pp. 53-67
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  • Fan, X., Boundary trace embedding theorems for variable exponent Sobolev spaces (2008) J. Math. Anal. Appl., 339 (2), pp. 1395-1412
  • Harjulehto, P., Hästö, P., Sobolev inequalities with variable exponent attaining the values 1 and n (2008) Publ. Mat., 52 (2), pp. 347-363
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  • Villani, C., (2003) Topics in Optimal Transportation, Volume 58 of Graduate Studies in Mathematics, , American Mathematical Society, Providence
  • (2009) Optimal Transport, Volume 338 of Grundlehren der Mathematischen Wissenschaften (Fundamental Principles of Mathematical Sciences), , Villani, C., Springer, Berlin (old and new)

Citas:

---------- APA ----------
Borthagaray, J.P., Fernández Bonder, J. & Silva, A. (2016) . A mass transportation approach for Sobolev inequalities in variable exponent spaces. Manuscripta Mathematica, 151(1-2), 133-146.
http://dx.doi.org/10.1007/s00229-016-0830-6
---------- CHICAGO ----------
Borthagaray, J.P., Fernández Bonder, J., Silva, A. "A mass transportation approach for Sobolev inequalities in variable exponent spaces" . Manuscripta Mathematica 151, no. 1-2 (2016) : 133-146.
http://dx.doi.org/10.1007/s00229-016-0830-6
---------- MLA ----------
Borthagaray, J.P., Fernández Bonder, J., Silva, A. "A mass transportation approach for Sobolev inequalities in variable exponent spaces" . Manuscripta Mathematica, vol. 151, no. 1-2, 2016, pp. 133-146.
http://dx.doi.org/10.1007/s00229-016-0830-6
---------- VANCOUVER ----------
Borthagaray, J.P., Fernández Bonder, J., Silva, A. A mass transportation approach for Sobolev inequalities in variable exponent spaces. Manuscr. Math. 2016;151(1-2):133-146.
http://dx.doi.org/10.1007/s00229-016-0830-6