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Stability for the Sobolev inequality with explicit constants

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Abstract

A quantitative version of the Bianchi--Egnell inequality concerning the stability of the Sobolev inequality is proved with explicit constants. For the proof we study a flow that interpolates continuously between a function and its symmetric decreasing rearrangement.
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Dates and versions

hal-03780031 , version 1 (18-09-2022)
hal-03780031 , version 2 (11-10-2022)
hal-03780031 , version 3 (29-12-2022)

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Jean Dolbeault, Maria J. Esteban, Rupert L. Frank, Michael Loss, Alessio Figalli. Stability for the Sobolev inequality with explicit constants. 2022. ⟨hal-03780031v2⟩
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