Stability for the Sobolev inequality in cones

Fuente: arXiv
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Autori principali: Pacella, Filomena, Ciraolo, Giulio, Polvara, Camilla Chiara
Natura: Preprint
Pubblicazione: 2025
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author Pacella, Filomena
Ciraolo, Giulio
Polvara, Camilla Chiara
author_facet Pacella, Filomena
Ciraolo, Giulio
Polvara, Camilla Chiara
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2502_11087
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Stability for the Sobolev inequality in cones
Pacella, Filomena
Ciraolo, Giulio
Polvara, Camilla Chiara
Analysis of PDEs
49J40, 26D10, 35A23, 35J91, 35B33
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.
title Stability for the Sobolev inequality in cones
topic Analysis of PDEs
49J40, 26D10, 35A23, 35J91, 35B33
url https://arxiv.org/abs/2502.11087