arXiv:2211.13180 Abstract | arXiv Analytics

arXiv:2211.13180 [math.AP]Abstract References Reviews Resources

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

Giovanni Brigati, Jean Dolbeault, Nikita Simonov

Published 2022-11-23Version 1

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.

Categories: math.AP, math.FA

Subjects: 26D10, 58J99, 39B62, 43A90, 49J40, 46E35

Keywords: constructive stability results, interpolation inequalities, nonlinear diffusion flows, logarithmic sobolev inequality, spectral decomposition techniques

Related articles: Most relevant | Search more

arXiv:2202.09693 [math.AP] (Published 2022-02-19, updated 2022-05-29)

Constructive stability results in interpolation inequalities and explicit improvements of decay rates of fast diffusion equations

Matteo Bonforte, Jean Dolbeault, Bruno Nazaret, Nikita Simonov

arXiv:1702.04390 [math.AP] (Published 2017-02-14)

Logarithmic Sobolev inequality revisited

Hoai-Minh Nguyen, Marco Squassina

arXiv:2409.14102 [math.AP] (Published 2024-09-21)

On some interpolation inequalities between Hölder and Lebesgue's spaces