Mappings of finite distortion: The zero set of the Jacobian

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Mappings of finite distortion: Capacity and modulus inequalities (2006, background): “Indeed, an example from [15] shows that, given any A so that the integral at (A-1) converges, one can construct a bounded, continuous, non-constant mapping of finite distortion that satisfies condition (A) for this A with K ≡ 1 outside a compact set.”
Extremal Mappings of Finite Distortion (2005, background): “It is shown in [19] that in fact Jðx; fÞ > 0 almost everywhere, so the addition of the integral over the set where Jðx; fÞ 1⁄4 0 is redundant.”
A note on extremal mappings of finite distortion (2005, unknown): “Combining (8) and (9) with the estimate |∇v(y)| Cr we find that the integral ∫”
Regularity of the Inverse of a Planar Sobolev Homeomorphism (2006, background): “[ 21 ]) that these assumptions guarantee that Jf(x) > 0 a.e.”
Hyperelastic Deformations of Smallest Total Energy (2009, background): “For instance this is the case when h is a homeomorphism with K I (x, h) ∈ L 1 (X) ,s ee [ 39 ].”