
Journal of Convex Analysis 28 (2021), No. 2, 549568 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. [ Fulltextpdf (169 KB)] for subscribers only. 