## 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

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