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.
Brigati, G., Dolbeault, J., Simonov, N. (2024). Logarithmic Sobolev and interpolation inequalities on the sphere: Constructive stability results. ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE, 41(5), 1289-1321 [10.4171/AIHPC/106].
Logarithmic Sobolev and interpolation inequalities on the sphere: Constructive stability results
Brigati, G;
2024
Abstract
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.
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