Work

Stability for the Sobolev inequality in cones

Year: 2025

Type: article

Abstract: We prove a quantitative Sobolev inequality in cones of Bianchi-Egnell type, which implies a stability property. Our result holds for any cone as long as the minimizers of the Sobolev quotient are nondegenerate,which is the case of most cones. When the minimizers are the classical bubbles we have more precise results. Finally, we show that local estimates are not enough to get the optimal constant for the quantitative Sobolev inequality.

Source: Journal of Differential Equations

DOI: 10.1016/j.jde.2025.113325

Authors: Giulio Ciraolo, Filomena Pacella, Camilla Chiara Polvara

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", European Commission, Ministero dell’Istruzione, dell’Università e della Ricerca, Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni

Award: G4550146497