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

By Veronica Felli, Matthias Schneider. 2002

158 citations recorded by the source corpus.

Abstract We find for small e positive solutions to the equation − div (|x| −2a ∇ u)− λ |x| 2(1+a) u=(1+ek(x)) u 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.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/69b9ab60c3482ee620cfc714fd30338a8e95b1e9

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

The role of Onofri type inequalities in the symmetry properties of extremals for Caffarelli-Kohn-Nirenberg inequalities, in two space dimensions (2008, background): “See [9, 11] for a discussion of the above eigenvalue problem.”
Elliptic Equations with Multi-Singular Inverse-Square Potentials and Critical Nonlinearity (2006, background): “( 1998 ), ( 2002 ), Egnell ( 1989 ), Felli and Schneider ( 2003 ), Ruiz and Willem ( 2003 ), and Smets ( 2005 ).”
Symmetry of extremal functions for the Caffarelli-Kohn-Nirenberg inequalities (2004, background): “In a recent preprint [9] of Felli and Schneider, it is observed that this curve h(a) can be sharpened to the following:”
On the Symmetry of Extremals for the Caffarelli-Kohn-Nirenberg Inequalities (2009, background): “On the other hand, extremals are known to be non radially symmetric for a certain range of parameters (a, b) identified first in [3] and subsequently improved in [6], given by the condition b bFS(a) , a 0 (see below).”