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arXiv · 2302.03926

On Gaussian interpolation inequalities

Giovanni Brigati·Jean Dolbeault·Nikita Simonov
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Abstract

This paper is devoted to Gaussian interpolation inequalities with endpoint cases corresponding to the Gaussian Poincar\'e and the logarithmic Sobolev inequalities, seen as limits in large dimensions of Gagliardo-Nirenberg-Sobolev inequalities on spheres. Entropy methods are investigated using not only heat flow techniques but also nonlinear diffusion equations as on spheres. A new stability result is established for the Gaussian measure, which is directly inspired by recent results for spheres.

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Giovanni Brigati, Jean Dolbeault, Nikita Simonov. 2023-02-08. On Gaussian interpolation inequalities. https://arxiv.org/abs/2302.03926

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