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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 ([email protected])
N. Jung
Affiliation:
Department of Mathematics, University of Illinois, Urbana, IL 61801, USA ([email protected])
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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

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