Advertisement

Singularities

  • Filip RindlerEmail author
Chapter
  • 3.2k Downloads
Part of the Universitext book series (UTX)

Abstract

All of the existence theorems for minimizers of integral functionals defined on Sobolev spaces \(\mathrm {W}^{1,p}(\varOmega ;\mathbb {R}^m)\) that we have seen so far required that \(p > 1\). Extending the existence theory to the linear-growth case \(p=1\) turns out to be quite intricate and necessitates the development of new tools.

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Mathematics InstituteUniversity of WarwickCoventryUK

Personalised recommendations