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Springer, Calculus of Variations and Partial Differential Equations, 3(54), p. 2465-2481, 2015

DOI: 10.1007/s00526-015-0871-9

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Rigidity results with applications to best constants and symmetry of Caffarelli-Kohn-Nirenberg and logarithmic Hardy inequalities

Journal article published in 2015 by Jean Dolbeault ORCID, Maria J. Esteban, Stathis Filippas, Achilles Tertikas
This paper is available in a repository.
This paper is available in a repository.

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Abstract

We take advantage of a rigidity result for the equation satisfied by an extremal function associated with a special case of the Caffarelli-Kohn-Nirenberg inequalities to get a symmetry result for a larger set of inequali-ties. The main ingredient is a reparametrization of the solutions to the Euler-Lagrange equations and estimates based on the rigidity result. The symmetry results cover a range of parameters which go well beyond the one that can be achieved by symmetrization methods or comparison techniques so far.