Stability for the Affine Sobolev Inequality and its Critical Points for $p\ge 2$

Rupert L. Frank; Yinqin Li; Dachun Yang

Stability for the Affine Sobolev Inequality and its Critical Points for $p\ge 2$

Analysis of PDEs 2026-07-07 v1 Classical Analysis and ODEs Functional Analysis

Authors: Rupert L. Frank , Yinqin Li , Dachun Yang

Abstract

We prove stability for the affine Sobolev inequality for exponents $p\geq 2$ with best possible norm and best possible stability exponent. We prove a corresponding results for critical points of the functional in the absence of bubbling.

Keywords

affine sobolev inequality stability critical points best constant bubbling

Cite

@article{arxiv.2607.06415,
  title  = {Stability for the Affine Sobolev Inequality and its Critical Points for $p\ge 2$},
  author = {Rupert L. Frank and Yinqin Li and Dachun Yang},
  journal= {arXiv preprint arXiv:2607.06415},
  year   = {2026}
}

Comments

56 pages