J.Onninen, A note on extremal mappings of finite distortion

We consider Sobolev mappings f ∈ W 1,1loc (Ω,R2), where Ω is a subdomain of R2. Thus, for almost every x ∈ Ω, we can speak of the linear transform Df(x): R2 → R2, called the differential of f at the point x. The Jacobian determinant J(x, f) is the determinant of the matrix Df(x), J(x, f) = detDf(x). We sa