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arXiv · 2605.28982

Qualitative stability for a family of trace Sobolev inequalities

Robin Neumayer
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Abstract

The goal of this short note is to prove qualitative stability for a family of trace Sobolev inequalities first proven by Carlen \& Loss for $p=2$ and by Maggi and the author for $p\in (1,n)$. This answers an open problem raised in a recent paper of Fan, Li \& Zhang, and in conjunction with their local analysis, yields sharp quantitative stability for this family of inequalities when $p=2$.

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Robin Neumayer. 2026-05-27. Qualitative stability for a family of trace Sobolev inequalities. https://arxiv.org/abs/2605.28982

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