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.

On BV Homeomorphisms

D'Onofrio L.;
2021

Abstract

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11367/100436
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