Description

• Title:
  A one dimensional problem related to the symmetry of minimisers for the Sobolev trace constant in a ball
• Creator:
  Torné, Olaf
• Description:
  The symmetry of minimisers for the best constant in the trace inequality in a ball, $S_q(\rho)=\inf_{u\in W^{1,p}(B_\rho)} \|u\|^p_{W^{1,p}(B_\rho)}/ \|u\|^{p}_{L^q(\partial B(\rho))}$ has been studied by various authors. Partial results are known which imply radial symmetry of minimisers, or lack thereof, depending on the values of trace exponent $q$ and the radius of the ball $\rho$. In this work we consider a one dimensional analogue of the trace inequality and the corresponding minimisation problem for the best constant. We describe the exact values of $q$ and $\rho$ for which minimisers are symmetric. We also consider the behaviour of minimisers as the symmetry breaking threshold for $q$ and $\rho$ is breached, and show a case in which both symmetric and nonsymmetric minimisers coexist.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2011.04.23
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 38, No 2 (December 2011); 363 - 372;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2011.037/8427
• Subject:
  Trace inequality;
  symmetry;
  symmetry breaking;
  35J20;
  26D15;
  35A30;
  35J60;
  47J30
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2011.037
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other