Logarithmic Sobolev Inequalities: A review on stability and instability results Brigati, Giovanni Dolbeault, Jean Simonov, Nikita ddc:510 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. Springer Nature 2026 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/21018 https://research-explorer.ista.ac.at/download/21018/21025 Brigati G, Dolbeault J, Simonov N. Logarithmic Sobolev Inequalities: A review on stability and instability results. <i>La Matematica</i>. 2026;5. doi:<a href="https://doi.org/10.1007/s44007-025-00180-y">10.1007/s44007-025-00180-y</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1007/s44007-025-00180-y info:eu-repo/semantics/altIdentifier/issn/2730-9657 info:eu-repo/semantics/altIdentifier/arxiv/2504.08658 https://creativecommons.org/licenses/by/4.0/ info:eu-repo/semantics/openAccess