Journal of Convex Analysis 28 (2021), No. 2, 549--568
Copyright Heldermann Verlag 2021
On BV Homeomorphisms
Luigi D'Onofrio
Dip. di Scienze e Tecnologie, Università degli Studi di Napoli "Parthenope", Napoli, Italy
donofrio@uniparthenope.it
Jan Malý
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", Università degli Studi di Napoli "Federico II", Napoli, Italy
sbordone@unina.it
Roberta Schiattarella
Dip. di Matematica e Applicazioni "R. Caccioppoli", Università 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.
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