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arXiv · 2502.11087

Stability for the Sobolev inequality in cones

Filomena Pacella·Giulio Ciraolo·Camilla Chiara Polvara
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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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Filomena Pacella, Giulio Ciraolo, Camilla Chiara Polvara. 2025-02-16. Stability for the Sobolev inequality in cones. https://arxiv.org/abs/2502.11087

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