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arXiv · 1412.0608

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

Jean Dolbeault·Maria J. Esteban·Stathis Filippas·Achiles Tertikas
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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.

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Jean Dolbeault, Maria J. Esteban, Stathis Filippas, Achiles Tertikas. 2014-12-01. Rigidity results with applications to best constants and symmetry of Caffarelli-Kohn-Nirenberg and logarithmic Hardy inequalities. https://arxiv.org/abs/1412.0608

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