Sobolev homeomorphisms are dense in volume preserving automorphisms

Azevedo, Assis; Azevedo, Davide; Bessa, Mário; Torres, Maria Joana

http://hdl.handle.net/10400.2/13847

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In 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.