Logarithmic Sobolev and interpolation inequalities on the sphere: constructive stability results
Giovanni Brigati, Jean Dolbeault, Nikita Simonov · arXiv (Cornell University) · 2022
We consider Gagliardo-Nirenberg inequalities on the sphere which interpolate between the Poincaré inequality and the Sobolev inequality, and include the logarithmic Sobolev inequality as a special case. We establish explicit stability results in the subcritical regime using spectral decomposition techniques, and entropy and carré du champ methods applied to nonlinear diffusion flows.