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Sobolev and isoperimetric inequalities with monomial weights

Autor
Cabre, X.; Ros, X.
Tipus d'activitat
Article en revista
Revista
Journal of differential equations
Data de publicació
2013
Volum
255
Número
11
Pàgina inicial
4312
Pàgina final
4336
DOI
https://doi.org/10.1016/j.jde.2013.08.010 Obrir en finestra nova
Repositori
http://hdl.handle.net/2117/20621 Obrir en finestra nova
URL
http://www.sciencedirect.com/science/article/pii/S0022039613003677# Obrir en finestra nova
Resum
We consider the monomial weight |x1|A1¿|xn|An in Rn, where Ai=0 is a real number for each i=1, n, and establish Sobolev, isoperimetric, Morrey, and Trudinger inequalities involving this weight. They are the analogue of the classical ones with the Lebesgue measure dx replaced by |x1|A1¿|xn|Andx, and they contain the best or critical exponent (which depends on A1, An). More importantly, for the Sobolev and isoperimetric inequalities, we obtain the best constant and extremal functions.When Ai are...
Citació
Cabre, X.; Ros, X. Sobolev and isoperimetric inequalities with monomial weights. "Journal of differential equations", 2013, vol. 255, núm. 11, p. 4312-4336.
Paraules clau
Axial symmetries Isoperimetric inequalities with a density Monomial weight Weighted Sobolev inequality
Grup de recerca
EDP - Equacions en Derivades Parcials i Aplicacions

Participants