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

  • Giovanni Brigati

    Université Paris-Dauphine – PSL Research University, Paris 16, France

  • Jean Dolbeault

    Université Paris-Dauphine – PSL Research University, Paris 16, France

  • Nikita Simonov

    Sorbonne Université, Paris, France
Logarithmic Sobolev and interpolation inequalities on the sphere: Constructive stability results cover
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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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Giovanni Brigati, Jean Dolbeault, Nikita Simonov, Logarithmic Sobolev and interpolation inequalities on the sphere: Constructive stability results. Ann. Inst. H. Poincaré C Anal. Non Linéaire (2023), published online first

DOI 10.4171/AIHPC/106