Azevedo, AssisAzevedo, DavideBessa, MárioTorres, Maria Joana2023-05-252023-05-252019A. Azevedo, D.Azevedo, M. Bessa, M.J. Torres, Sobolev homeomorphisms are dense in volume preserving automorphisms, 276, 10, 3261-3274, 20190022-1236http://hdl.handle.net/10400.2/13847In this paper we prove a weak version of Lusin’s theorem for the space of Sobolev-(1,p) volume preserving homeomor- phisms on closed and connected n-dimensional manifolds, n ≥ 3, for p < n − 1. We also prove that if p > n this result is not true. More precisely, we obtain the density of Sobolev-(1,p) homeomorphisms in the space of volume pre- serving automorphisms, for the weak topology. Furthermore, the regularization of an automorphism in a uniform ball cen- tered at the identity can be done in a Sobolev-(1, p) ball with the same radius centered at the identity.engLusin theoremVolume preservingSobolev homeomorphismjournal article10.1016/j.jfa.2018.10.008