skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.


This content will become publicly available on June 1, 2026

Title: Degenerate Sobolev inequalities from the classical Sobolev inequality
Award ID(s):
2349550
PAR ID:
10601295
Author(s) / Creator(s):
; ; ;
Publisher / Repository:
Springer Nature
Date Published:
Journal Name:
Analysis and Mathematical Physics
Volume:
15
Issue:
3
ISSN:
1664-2368
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. null (Ed.)
  2. Abstract We give a full characterization of circle homeomorphisms which admit a homeomorphic extension to the unit disk with finite bi-Sobolev norm. As a special case, a bi-conformal variant of the famous Beurling–Ahlfors extension theorem is obtained. Furthermore we show that the existing extension techniques such as applying either the harmonic or the Beurling–Ahlfors operator work poorly in the degenerated setting. This also gives an affirmative answer to a question of Karafyllia and Ntalampekos. 
    more » « less