We find positive solutions to critical elliptic equations of Caffarelli-Kohn-Nirenberg type 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.
Felli, V., Schneider, M. (2003). Perturbation results of critical elliptic equations of Caffarelli-Kohn-Nirenberg type. JOURNAL OF DIFFERENTIAL EQUATIONS, 191(10), 121-142 [10.1016/S0022-0396(02)00085-2].
Perturbation results of critical elliptic equations of Caffarelli-Kohn-Nirenberg type
FELLI, VERONICA;
2003
Abstract
We find positive solutions to critical elliptic equations of Caffarelli-Kohn-Nirenberg type 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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