Qualitative stability for a family of trace Sobolev inequalities
Analysis of PDEs
2026-05-29 v1
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 and by Maggi and the author for . 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 .
Keywords
Cite
@article{arxiv.2605.28982,
title = {Qualitative stability for a family of trace Sobolev inequalities},
author = {Robin Neumayer},
journal= {arXiv preprint arXiv:2605.28982},
year = {2026}
}