Jacobians of Sobolev homeomorphisms

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Smooth approximation of bi-Lipschitz orientation-preserving homeomorphisms (2011, result): “Actually, the result by Hencl and Koskela is even stronger, since it states that for a W 1,1 map one has that u−1 ∈ W 1,1 if and only if u has finite distorsion; the study of maps of finite distorsion in connection with Sobolev homeomorphisms is very active in last years, see for instance [10,16,15,”
Existence of energy-minimal diffeomorphisms between doubly connected domains (2010, background): “morphisms of the Sobolev class W1,1 loc (Ω) this implies that the Jacobian determinant does not change sign: it is either nonnegative or nonpositive at almost every point [3, Theorem 3.3.4], see also [12]. The homeomorphisms considered in this paper are sense-preserving unless stated otherwise. Let ”
Lectures on Mappings of Finite Distortion (2014, result): “We give a detailed proof under the assumption that p > n − 1 and we recall the result of Hencl and Malý [15].”