Jan Mal\'y
$L^p$-approximation of Jacobians

Comment.Math.Univ.Carolinae 32,4 (1991) 659-666.

Abstract:The paper investigates the nonlinear function spaces introduced by Giaquinta, Modica and Sou\v cek. It is shown that a function from $Cart^p(\Omega ,\bold R^m)$ is approximated by $\Cal C ^1$ functions strongly in $\Cal A^q(\Omega ,\bold R^m)$ whenever $q<p$. An example is shown of a function which is in $cart^p(\Omega ,\bold R^2)$ but not in $cart^p(\Omega ,\bold R^2)$.

Keywords: Sobolev spaces, minors of the Jacobi matrix, weak and strong convergence, cartesian currents
AMS Subject Classification: 28A75, 73C50