Abstract for the talk on 17.07.2018 (16:45 h)

Oberseminar ANALYSIS - PROBABILITY

Michael Loss (Georgia Institute of Technology)
The phase diagram of the Caffarelli-Kohn-Nirenberg inequalities

The Caffarelli-Kohn-Nirenberg inequalities form a two parameter family of

inequalities

that interpolate between Sobolev's inequality and Hardy's inequality. The

functional

whose minimization yields the sharp constant is invariant under rotations.

It has been known for some time that there is a region in parameter space

where the optimizers

for the sharp constant are not radial. In this talk I indicate a proof

that, in the remaining

parameter region, the optimizers are in fact radial.

The proof will proceed via a well chosen flow that decreases the functional

unless the

function is a radial optimizer. This is joint work with Jean Dolbeault and

Maria Esteban.