Journal Home Page

Cumulative Index

List of all Volumes

Complete Contents
of this Volume

Previous Article

Next Article
 


Journal of Convex Analysis 28 (2021), No. 2, [final page numbers not yet available]
Copyright Heldermann Verlag 2021



On BV Homeomorphisms

Luigi D'Onofrio
Dip. di Scienze e Tecnologie, UniversitÓ degli Studi di Napoli "Parthenope", Napoli, Italy
donofrio@uniparthenope.it

Jan Malř
Dept. of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic
maly@karlin.mff.cuni.cz

Carlo Sbordone
Dip. di Matematica e Applicazioni "R. Caccioppoli", UniversitÓ degli Studi di Napoli "Federico II", Napoli, Italy
sbordone@unina.it

Roberta Schiattarella
Dip. di Matematica e Applicazioni "R. Caccioppoli", UniversitÓ degli Studi di Napoli "Federico II", Napoli, Italy
roberta.schiattarella@unina.it



We obtain the rectifiability of the graph of a bounded variation homeomorphism f in the plane and relations between gradients of f and its inverse. Further, we show an example of a bounded variation homeomorphism f in the plane which satisfies the (N) and (N-1) properties and strict positivity of Jacobian of both itself and its inverse, but neither f nor f-1 is Sobolev.

Keywords: Bounded variation homeomorphisms, rectifiability of the graph, distributional Jacobian.

MSC: 26B30, 49Q15, 58A25, 46E35.

[ Fulltext-pdf  (170  KB)] for subscribers only.