Extremal functions in some interpolation inequalities: Symmetry, symmetry breaking and estimates of the best constants
Jean Dolbeault (CEREMADE), Maria J. Esteban (CEREMADE)
TL;DR
This paper reviews recent findings on the existence, symmetry, and symmetry breaking of optimal functions in certain interpolation inequalities, highlighting new perspectives and collaborations.
Contribution
It provides a new viewpoint on symmetry properties and best constants in Caffarelli-Kohn-Nirenberg and weighted logarithmic Hardy inequalities.
Findings
Identification of conditions for symmetry and symmetry breaking
New estimates for the best constants in inequalities
Collaborative insights into optimal functions
Abstract
This contribution is devoted to a review of some recent results on existence, symmetry and symmetry breaking of optimal functions for Caffarelli-Kohn-Nirenberg and weighted logarithmic Hardy inequalities. These results have been obtained in a series of papers in collaboration with M. del Pino, S. Filippas, M. Loss, G. Tarantello and A. Tertikas and are presented from a new viewpoint.
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