Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-17T19:58:04.159Z Has data issue: false hasContentIssue false
  • English
  • Français

Asymptotic expansions and extremals for the critical Sobolev and Gagliardo–Nirenberg inequalities on a torus

Published online by Cambridge University Press:  22 May 2013

Michele Bartuccelli ,
Jonathan Deane  and
Sergey Zelik
Michele Bartuccelli
Affiliation:
University of Surrey, Department of Mathematics, Guildford GU2 7XH, UK ([email protected]; [email protected]; [email protected])
Jonathan Deane
Affiliation:
University of Surrey, Department of Mathematics, Guildford GU2 7XH, UK ([email protected]; [email protected]; [email protected])
Sergey Zelik
Affiliation:
University of Surrey, Department of Mathematics, Guildford GU2 7XH, UK ([email protected]; [email protected]; [email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

We present a comprehensive study of interpolation inequalities for periodic functions with zero mean, including the existence of and the asymptotic expansions for the extremals, best constants, various remainder terms, etc. Most attention is paid to the critical (logarithmic) Sobolev inequality in the two-dimensional case, although a number of results concerning the best constants in the algebraic case and different space dimensions are also obtained.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 143 , Issue 3 , June 2013 , pp. 445 - 482
Copyright
Copyright © Royal Society of Edinburgh 2013 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)