Geodesic
On BV Homeomorphisms
Journal of convex analysis, Tome 28 (2021) no. 2, pp. 549-568
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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.
Classification : 26B30, 49Q15, 58A25, 46E35
Mots-clés : Bounded variation homeomorphisms, rectifiability of the graph, distributional Jacobian 
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     author = {L. D'Onofrio and J. Mal\'y and C. Sbordone and R. Schiattarella},
     title = {On {BV} {Homeomorphisms}},
     journal = {Journal of convex analysis},
     pages = {549--568},
     year = {2021},
     volume = {28},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JCA_2021_28_2_JCA_2021_28_2_a13/}
}
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L. D'Onofrio; J. Malý; C. Sbordone; R. Schiattarella. On BV Homeomorphisms. Journal of convex analysis, Tome 28 (2021) no. 2, pp. 549-568. http://geodesic.mathdoc.fr/item/JCA_2021_28_2_JCA_2021_28_2_a13/