BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

Why in some cases the asymptotic linearized problem yields optimal results for a nonlinear version of the carré du champ Esteban, Maria J.


Using a nonlinear parabolic flow, in this talk I will explain why the optimal regions of symmetry and symmetry breaking for the extremals of critical and subcritical Caffarelli-Kohn-Nirenberg inequalities are related to the spectral gap of the linearized problem around the asymptotic Barenblatt solutions. This is a surprising result since it means that a global test yields a global result. The use of the parabolic flow also allows to get improved inequalities with explicit remainder terms.

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