A Sobolev inequality with reciprocal weights

A Sobolev inequality with reciprocal weights

We give a Sobolev inequality with the weight K(x) belonging to the class A2∩Gn for the function |u|t and the weight K(x)−1 for |∇u|2. The constant in the relevant inequality is seen to depend on the Gn and A2 constants of the weight.

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Veröffentlicht in:Nonlinear analysis 2012-09, Vol.75 (13), p.5348-5356
Hauptverfasser: Alberico, Angela, Alberico, Teresa, Sbordone, Carlo
Format: Artikel
Sprache:eng
Schlagworte:
Fractional integrals
Inequalities
Muckenhoupt and Gehring classes
Nonlinearity
Sobolev inequalities
Weighted inequalities
Weights
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Zusammenfassung:We give a Sobolev inequality with the weight K(x) belonging to the class A2∩Gn for the function |u|t and the weight K(x)−1 for |∇u|2. The constant in the relevant inequality is seen to depend on the Gn and A2 constants of the weight.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2012.04.049