English

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 p=2p=2 and by Maggi and the author for p(1,n)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=2p=2.

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}
}