Sharp gradient stability for the Sobolev inequality

By Alessio Figalli, Y. Zhang. Duke mathematical journal, 2020

112 citations recorded by the source corpus.

Motivated by important applications to problems in the calculus of variations and evolution PDEs, in recent years there has been a growing interest around the understanding of quantitative stability for functional/geometric inequalities, see for instance [3, 2, 8, 27, 28, 21, 9, 22, 29, 18, 10, 6, 7, 11, 13, 19, 23, 35, 26, 5, 14, 16, 17, 20, 25, 30, 31, 24, 33, 34], as well as the survey papers [15, 26, 17]. Following this line of research, in this paper we shall investigate the stability of minimizers to the classical Sobolev inequality.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1b9c6bb359d9828d7d05bb0ad85de919dbed8b48

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Sharp stability for Sobolev and log-Sobolev inequalities, with optimal dimensional dependence (2022, background): “In fact, stability has attracted a lot of attention in recent years and we refer to [44, 26, 39, 27, 23, 30, 21, 24, 38, 25, 61, 42, 43, 40, 10] and the references within for a list of works in this direction.”
Sharp quantitative estimates of Struwe’s decomposition (2021, unknown): “4) to Sobolev inequality with general exponents we refer to Figalli and Neumayer [21], Figalli and Zhang [22] and the references therein.”