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arXiv · 2211.13180

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

Giovanni Brigati·Jean Dolbeault·Nikita Simonov
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Abstract

We consider Gagliardo-Nirenberg inequalities on the sphere which interpolate between the Poincar\'e 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 carr\'e du champ methods applied to nonlinear diffusion flows.

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Giovanni Brigati, Jean Dolbeault, Nikita Simonov. 2022-11-23. Logarithmic Sobolev and interpolation inequalities on the sphere: constructive stability results. https://arxiv.org/abs/2211.13180

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