Geodesic
$L^p$-approximation of Jacobians
Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) no. 4, pp. 659-666

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The paper investigates the nonlinear function spaces introduced by Giaquinta, Modica and Souček. It is shown that a function from $\operatorname{Cart}^p(\Omega ,\bold R^m)$ is approximated by $\Cal C ^1$ functions strongly in $\Cal A^q(\Omega ,\bold R^m)$ whenever $q$. An example is shown of a function which is in $\operatorname{cart}^p(\Omega ,\bold R^2)$ but not in $\operatorname{cart}^p(\Omega ,\bold R^2)$.
Classification : 28A75, 46E40, 49J45, 73C50, 74B20
Keywords: Sobolev spaces; minors of the Jacobi matrix; weak and strong convergence; cartesian currents 
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     author = {Mal\'y, Jan},
     title = {$L^p$-approximation of {Jacobians}},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {659--666},
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     volume = {32},
     number = {4},
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Malý, Jan. $L^p$-approximation of Jacobians. Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) no. 4, pp. 659-666. http://geodesic.mathdoc.fr/item/CMUC_1991__32_4_a7/