Perturbation results of critical elliptic equations of Caffarelli-Kohn-Nirenberg type

2002/03/20 by Veronica Felli, Matthias Schneider, Felli, Veronica +1 · 4 citations
Mathematics · #35B20 #35B33 #35J20 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #math.AP #math.FA #msc:35B20 #msc:35B33 #msc:35J20

paper · pdf · doi:10.48550/arxiv.math/0203208

15 pages, 4 figures

arxiv created 2002/07/12 · arxiv updated 2009/11/30

Abstract

We find for small ε positive solutions to the equation -\textrmdiv (|x|^-2a∇ u)-\fracλ|x|^2(1+a) u= (1+εk(x))\fracu^p-1|x|^bp in ℝ^N, which branch off from the manifold of minimizers in the class of radial functions of the corresponding Caffarelli-Kohn-Nirenberg type inequality. Moreover, our analysis highlights the symmetry-breaking phenomenon in these inequalities, namely the existence of non-radial minimizers.

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