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Abstract:

In this paper we analyze the following elliptic problem related to some Caffarelli-Kohn-Nirenberg inequalities: where is a domain such that 0 and c; p are positive constants verifying 0 < and p > Our study concerns to existence of solutions to the former problem. More precisely, first we determine a critical thereshold for the power p, in the sense that, beyond this value it does not exist any positive supersolution to our problem, not even in a very weak sense. In addition, we show existence of solutions for all the values 0 below this threshold, with the restriction whenever the righthand side verifies if When it suffices that The existence of solutions for is an open question.

Registro:

Documento: Artículo
Título:Optimal power for an elliptic equation related to some caffarelli-kohn-nirenberg inequalities
Autor:Perez-Llanos, M.
Filiación:Instituto de Investigaciones Mateḿaticas Luis Santaĺo, CONICET, Facultad de Ciencias Exactas y Naturales, Pabelĺon i Ciudad Universitaria1428, Argentina
Palabras clave:Caffarelli-Kohn-Nirenberg inequality; Hardy potential; Weighted Sobolev Spaces
Año:2016
Volumen:15
Número:6
Página de inicio:1975
Página de fin:2005
DOI: http://dx.doi.org/10.3934/cpaa.2016024
Título revista:Communications on Pure and Applied Analysis
Título revista abreviado:Commun. Pure Appl. Anal.
ISSN:15340392
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15340392_v15_n6_p1975_PerezLlanos

Referencias:

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Citas:

---------- APA ----------
(2016) . Optimal power for an elliptic equation related to some caffarelli-kohn-nirenberg inequalities. Communications on Pure and Applied Analysis, 15(6), 1975-2005.
http://dx.doi.org/10.3934/cpaa.2016024
---------- CHICAGO ----------
Perez-Llanos, M. "Optimal power for an elliptic equation related to some caffarelli-kohn-nirenberg inequalities" . Communications on Pure and Applied Analysis 15, no. 6 (2016) : 1975-2005.
http://dx.doi.org/10.3934/cpaa.2016024
---------- MLA ----------
Perez-Llanos, M. "Optimal power for an elliptic equation related to some caffarelli-kohn-nirenberg inequalities" . Communications on Pure and Applied Analysis, vol. 15, no. 6, 2016, pp. 1975-2005.
http://dx.doi.org/10.3934/cpaa.2016024
---------- VANCOUVER ----------
Perez-Llanos, M. Optimal power for an elliptic equation related to some caffarelli-kohn-nirenberg inequalities. Commun. Pure Appl. Anal. 2016;15(6):1975-2005.
http://dx.doi.org/10.3934/cpaa.2016024