Description

• Title:
  Minimizers and symmetric minimizers for problems with critical Sobolev exponent
• Creator:
  Waliullah, Shoyeb
• Description:
  In this paper we will be concerned with the existence and non-existence of constrained minimizers in Sobolev spaces $D^{k,p}({\mathbb R}^N)$, where the constraint involves the critical Sobolev exponent. Minimizing sequences are not, in general, relatively compact for the embedding $D^{k,p}({\mathbb R}^N)\hookrightarrow L^{p^*} ({\mathbb R}^N,Q)$ when $Q$ is a non-negative, continuous, bounded function. However if $Q$ has certain symmetry properties then all minimizing sequences are relatively compact in the Sobolev space of appropriately symmetric functions. For $Q$ which does not have the required symmetry, we give a condition under which an equivalent norm in $D^{k,p}({\mathbb R}^N)$ exists so that all minimizing sequences are relatively compact. In fact we give an example of a $Q$ and an equivalent norm in $D^{k,p}({\mathbb R}^N)$ so that all minimizing sequences are relatively compact.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2009.12.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 34, No 2 (December 2009); 291 - 326;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2009.044/8634
• Subject:
  Concentration-compactness principle;
  critical Sobolev exponent;
  symmetric solutions of elliptic equations;
  Sobolev embeddings in weighted spaces;
  35J60
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2009.044
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other