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

Veronica Felli·Matthias Schneider
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Abstract

We find for small $ε$ positive solutions to the equation \[-\textrm{div} (|x|^{-2a}\nabla u)-\displaystyle{\fracλ{|x|^{2(1+a)}}} u= \Big(1+εk(x)\Big)\frac{u^{p-1}}{|x|^{bp}}\] in ${\mathbb{R}}^N$, 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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Veronica Felli, Matthias Schneider. 2002-07-12. Perturbation results of critical elliptic equations of Caffarelli-Kohn-Nirenberg type. https://arxiv.org/abs/math/0203208

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