Hostname: page-component-848d4c4894-nr4z6 Total loading time: 0 Render date: 2024-05-16T22:21:36.293Z Has data issue: false hasContentIssue false
  • English
  • Français

Strict convergence and minimal liftings in BV

Published online by Cambridge University Press:  12 July 2007

R. L. Jerrard  and
N. Jung
R. L. Jerrard
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Ontario M5S 3G3, Canada (rjerrard@math.toronto.edu)
N. Jung
Affiliation:
Department of Mathematics, University of Illinois, Urbana, IL 61801, USA (n-jung1@math.uiuc.edu)
Get access Rights & Permissions [Opens in a new window]

Abstract

Given a function υ ∈ BV (Ω; Rm), we introduce the notion of a minimal lifting of Dυ. We prove that every υ ∈ BV (Ω; Rm) has a unique minimal lifting, and we show that if υk → υ strictly in BV, then the minimal liftings of υk converge weakly as measures to the minimal lifting of υ. As an application, we deduce a result about weak continuity of the distributional determinant Det D2u with respect to strict convergence.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 134 , Issue 6 , December 2004 , pp. 1163 - 1176
Copyright
Copyright © Royal Society of Edinburgh 2004

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)