Description

• Title:
  Minimizing the Dirichlet energy over a space of measure preserving maps
• Creator:
  Taheri, Ali
• Description:
  Let $\Omega \subset \mathbb R^n$ be a bounded Lipschitz domain and consider the Dirichlet energy functional $$ {\mathbb F} [\u , \Omega] := \frac{1}{2} \int_\Omega |\nabla \u (\x )|^2 dx, $$ over the space of measure preserving maps $$ {\mathcal A}(\Omega)=\{\u \in W^{1,2}(\Omega, \mathbb R^n) : \u |_{\partial \Omega} = \x , \ \det \nabla \u = 1 \text{ ${\mathcal L}^n$-a.e in $\Omega$} \}. $$ Motivated by their significance in topology and the study of mapping class groups, in this paper we consider a class of maps, referred to as {\it twists}, and examine them in connection with the Euler-Lagrange equations associated with ${\mathbb F}$ over ${\mathcal A}(\Omega)$. We investigate various qualitative properties of the resulting solutions in view of a remarkably simple, yet seemingly unknown explicit formula, when $n=2$.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2009.03.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 33, No 1 (March 2009); 179 - 204;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2009.013/8652
• Subject:
  Dirichlet energy problem;
  variational methods;
  measure preserving maps;
  34A15;
  34K15
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2009.013
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other