Stability for the Sobolev inequality in cones

2025/02/16 by Filomena Pacella, Giulio Ciraolo, Pacella, Filomena +3 · 1 citation
Mathematics · #26D10 #35A23 #35B33 #35J91 #49J40 #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2502.11087

openalex publication_date 2025/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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• Bifurcation from bubbles in nonconvex cones

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