Logarithmic Sobolev and interpolation inequalities on the sphere: constructive stability results
Analysis of PDEs
2024-01-24 v4 Functional Analysis
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.
Cite
@article{arxiv.2211.13180,
title = {Logarithmic Sobolev and interpolation inequalities on the sphere: constructive stability results},
author = {Giovanni Brigati and Jean Dolbeault and Nikita Simonov},
journal= {arXiv preprint arXiv:2211.13180},
year = {2024}
}