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.

Contact details are reproduced from the original publication and may be historical.

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

L. D'Onofrio, J. Malý, C. Sbordone, R. Schiattarella. “On BV Homeomorphisms.” Journal of Convex Analysis 28 (2021), No. 2, 549–568.