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arxiv 2402.08527 v2 pith:IPMCLPNM submitted 2024-02-13 math.AP

Jean Dolbeault , Maria J. Esteban , Alessio Figalli , Rupert Frank , Michael Loss This is my paper · ORCID
classification math.AP
keywords inequalitysobolevstabilitygaussianinequalitiesinterpolationlogarithmicobtained
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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]. The stability for the Gaussian logarithmic Sobolev inequality was obtained as a byproduct of the stability for the Sobolev inequality. Here we give a new, direct, alternative proof. We also discuss improved versions of interpolation inequalities based on the carr\'e du champ method.

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  1. An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds

    math.AP 2024-12 accept novelty 2.0 of 10

    The paper reviews and re-exposes existing stability theorems for sharp Sobolev inequalities on manifolds with Ricci lower bounds.

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