Stability for the Sobolev inequality with explicit constants

Jean Dolbeault (1) , Maria J. Esteban (1) , Rupert L. Frank (2) , Michael Loss (3) , Alessio Figalli (4)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 LMU - Ludwig Maximilian University [Munich] = Ludwig Maximilians Universität München
3 Georgia Institute of Technology [Atlanta]
4 Department of Mathematics - ETH

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.

Mots clés: Sobolev inequality; stability; rearrangement; Steiner symmetrization

Domaines: Equations aux dérivées partielles [math.AP]

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