Sharp gradient stability for the Sobolev inequality

Alessio Figalli; Yi Ru-Ya Zhang

Sharp gradient stability for the Sobolev inequality

Functional Analysis 2020-03-10 v1

Authors: Alessio Figalli , Yi Ru-Ya Zhang

Abstract

We prove a sharp quantitative version of the $p$ -Sobolev inequality for any $1<p<n$ , with a control on the strongest possible distance from the class of optimal functions. Surprisingly, the sharp exponent is constant for $p<2$ , while it depends on $p$ for $p>2$ .

Keywords

sobolev inequalities sobolev spaces sobolev regularity of partial differential equations

Cite

@article{arxiv.2003.04037,
  title  = {Sharp gradient stability for the Sobolev inequality},
  author = {Alessio Figalli and Yi Ru-Ya Zhang},
  journal= {arXiv preprint arXiv:2003.04037},
  year   = {2020}
}

Comments

32 pages

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