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In this paper, we present recent stability results with explicit and dimensionally sharp constants and optimal norms for the Sobolev inequality and for the Gaussian logarithmic Sobolev inequality obtained by the authors in [24].
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Degenerate stability of some Sobolev inequalities
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Jean Dolbeault, Maria J. Esteban, and Michael Loss · 2014
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The deficit in the Gaussian log-Sobolev inequality and inverse Santaló inequalities
Nathael Gozlan · 2022
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Logarithmic Sobolev and interpolation inequalities on the sphere: Constructive stability results
Giovanni Brigati, Jean Dolbeault, and Nikita Simonov · 2023
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Stability of Hardy-Littlewood-Sobolev inequalities with explicit lower bounds
Lu Chen, Guozhen Lu, and Hanli Tang · 2023
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Sharp stability for Sobolev and log-Sobolev inequalities, with optimal dimensional dependence
Jean Dolbeault, Maria J. Esteban, Alessio Figalli, Rupert L. Frank, and Michael Loss · 2023
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On the sharp constant in the Bianchi–Egnell stability inequality
Tobias König · 2023
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On Gaussian interpolation inequalities
Giovanni Brigati, Jean Dolbeault, and Nikita Simonov · 2024
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Stability for the logarithmic Sobolev inequality
Giovanni Brigati, Jean Dolbeault, and Nikita Simonov · 2024
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