Lp estimates and asymptotic behavior for finite energy solutions of extremals to Hardy-Sobolev inequalities

2006/01/27 by Vassilev, Dimiter · 1 citation
#35B05 #35J65 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0601662

Abstract

Motivated by the equation satisfied by the extremals of certain Hardy-Sobolev type inequalities, we show sharp L^q regularity for finite energy solutions of p-laplace equations involving critical exponents and possible singularity on a sub-space of ℝⁿ, which imply asymptotic behavior of the solutions at infinity. In addition, we find the best constant and extremals in the case of the considered L² Hardy-Sobolev inequality.

Cited by

• Quasilinear problems with critical Sobolev exponent for the Grushin p-Laplace operator

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