Stability Results for Logarithmic Sobolev and Gagliardo–Nirenberg Inequalities

By Jean Dolbeault, Giuseppe Toscani. 2014

63 citations recorded by the source corpus.

This paper is devoted to improvements of functional inequalities based on scalings and written in terms of relative entropies. When scales are taken into account and second moments fixed accordingly, deficit functionals provide explicit stability measurements, i.e., bound with explicit constants distances to the manifold of optimal functions. Various results are obtained for the Gaussian logarithmic Sobolev inequality and its Euclidean counterpart, for the Gaussian generalized Poincare inequalities and for the Gagliardo-Nirenberg inequalities. As a consequence, faster convergence rates in diffusion equations (fast diffusion, Ornstein-Uhlenbeck and porous medium equations) are obtained.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/59d9a9070dbf751b6e1e7a84b90e0d51ec738e64

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Sharp stability for Sobolev and log-Sobolev inequalities, with optimal dimensional dependence (2022, background): “Other remainder terms are given in [8, 35, 32] and, using weaker notions of distances, in [8, 49, 35, 37, 48] while some obstructions to stability results involving strong notions of distance are given in [50, 34].”