Jacobians and Hardy spaces

Abstract: "Motivated by questions in nonlinear elasticity, Stefan Müller has recently proved that if u [epsilon] (W¹,N ([subscript R superscript N))[superscript N] satisfies J(u) = det[delta]u [> or =] 0 almost everywhere, then one has J(u)log(1+J (u)) L¹loc(R[superscript N]). This kind of result has been generalized in the context of Hardy spaces by R. Coifman and P.L. Lions and Y. Meyer and S. Semmes. The present report gives some elementary proofs, explained in the simple solution of R², of the embedding results of Jacobian determinants into Hardy spaces."