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
that interpolate between Sobolev's inequality and Hardy's inequality. The
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
function is a radial optimizer. This is joint work with Jean Dolbeault and