Logarithmic Sobolev and interpolation inequalities on the sphere: constructive stability results

Giovanni Brigati (1) , Jean Dolbeault (1) , Nikita Simonov (2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions

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.

Mots clés: logarithmic Sobolev inequality; Gagliardo-Nirenberg inequalities; stability; sphere; spectral decomposition

Domaines: Equations aux dérivées partielles [math.AP]

Giovanni Brigati, Jean Dolbeault, Nikita Simonov. Logarithmic Sobolev and interpolation inequalities on the sphere: constructive stability results. 2022. ⟨hal-03868496v1⟩