Logarithmic Sobolev Inequalities: A Review on Stability and Instability Results
Abstract
Abstract In this paper, we review recent results on stability and instability in logarithmic Sobolev inequalities, with a particular emphasis on strong norms. We consider several versions of these inequalities on the Euclidean space, for the Lebesgue and the Gaussian measures, and discuss their differences in terms of moments and stability. We give new and direct proofs, as well as examples and discuss the stability of a logarithmic uncertainty principle. Although we do not cover all aspects of the topic, we hope to contribute to establishing the state of the art.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Metallurgy and Material Forming
Differential Equations and Boundary Problems
Publication details
- Journal / source
- La Matematica
- Publisher
- Springer Science and Business Media LLC
- Volume
- 5
- Issue
- 1
- Publication date
- 8 January 2026
- Language
- EN