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Article Dans Une Revue Calculus of Variations and Partial Differential Equations Année : 2015

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

Résumé

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.
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Dates et versions

hal-01089318 , version 1 (01-12-2014)

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Jean Dolbeault, Maria J. Esteban, Stathis Filippas, Achiles Tertikas. Rigidity results with applications to best constants and symmetry of Caffarelli-Kohn-Nirenberg and logarithmic Hardy inequalities: Symmetry in Caffarelli-Kohn-Nirenberg and logarithmic Hardy inequalities. Calculus of Variations and Partial Differential Equations, 2015, pp.10.1007/s00526-015-0871-9. ⟨hal-01089318⟩
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