Parabolic methods for ultraspherical interpolation inequalities
Parabolic methods for ultraspherical interpolation inequalities
The carr\'e du champ method is a powerful technique for proving interpolation inequalities with explicit constants in presence of a non-trivial metric on a manifold. The method applies to some classical Gagliardo-Nirenberg-Sobolev inequalities on the sphere, with optimal constants. Very nonlinear regimes close to the critical Sobolev exponent can be …