Geodesic
$L^p$-approximation of Jacobians
Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) no. 4, pp. 659-666 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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
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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     title = {$L^p$-approximation of {Jacobians}},
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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/

[1] Giaquinta M., Modica G., Souček J.: Cartesian currents, weak dipheomorphisms and existence theorems in nonlinear elasticity. Arch. Rat. Mech. Anal. 106 (1989), 97-159. {Erratum and addendum}. Arch. Rat. Mech. Anal. 109 (1990), 385-592. | MR

[2] Giaquinta M., Modica G., Souček J.: Cartesian currents and variational problems for mappings into spheres. Annali S.N.S. Pisa 16 (1989), 393-485. | MR

[3] Giaquinta M., Modica G., Souček J.: The Dirichlet energy of mappings with values into the sphere. Manuscripta Math. 65 (1989), 489-507. | MR

[4] Giaquinta M., Modica G., Souček J.: The Dirichlet integral for mappings between manifolds: Cartesian currents and homology. Università di Firenze, preprint, 1991. | MR

[5] V. Šverák: Regularity properties of deformations with finite energy. Arch. Rat. Mech. Anal. 100 (1988), 105-127. | MR

[6] W.P. Ziemer: Weakly Differentiable Functions. Sobolev Spaces and Function of Bounded Variation. Graduate Text in Mathematics 120, Springer-Verlag, 1989. | MR