# ${L}^{p}$-approximation of Jacobians

Commentationes Mathematicae Universitatis Carolinae (1991)

- Volume: 32, Issue: 4, page 659-666
- ISSN: 0010-2628

## Access Full Article

top## Abstract

top## How to cite

topMalý, Jan. "$L^p$-approximation of Jacobians." Commentationes Mathematicae Universitatis Carolinae 32.4 (1991): 659-666. <http://eudml.org/doc/247295>.

@article{Malý1991,

abstract = {The paper investigates the nonlinear function spaces introduced by Giaquinta, Modica and Souček. It is shown that a function from $\operatorname\{Cart\}^p(\Omega ,\mathbf \{R\}^m)$ is approximated by $\mathcal \{C\} ^1$ functions strongly in $\mathcal \{A\}^q(\Omega ,\mathbf \{R\}^m)$ whenever $q<p$. An example is shown of a function which is in $\operatorname\{cart\}^p(\Omega ,\mathbf \{R\}^2)$ but not in $\operatorname\{cart\}^p(\Omega ,\mathbf \{R\}^2)$.},

author = {Malý, Jan},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {Sobolev spaces; minors of the Jacobi matrix; weak and strong convergence; cartesian currents; Sobolev space; approximation; smooth functions; nonlinear function spaces},

language = {eng},

number = {4},

pages = {659-666},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

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

url = {http://eudml.org/doc/247295},

volume = {32},

year = {1991},

}

TY - JOUR

AU - Malý, Jan

TI - $L^p$-approximation of Jacobians

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 1991

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 32

IS - 4

SP - 659

EP - 666

AB - The paper investigates the nonlinear function spaces introduced by Giaquinta, Modica and Souček. It is shown that a function from $\operatorname{Cart}^p(\Omega ,\mathbf {R}^m)$ is approximated by $\mathcal {C} ^1$ functions strongly in $\mathcal {A}^q(\Omega ,\mathbf {R}^m)$ whenever $q<p$. An example is shown of a function which is in $\operatorname{cart}^p(\Omega ,\mathbf {R}^2)$ but not in $\operatorname{cart}^p(\Omega ,\mathbf {R}^2)$.

LA - eng

KW - Sobolev spaces; minors of the Jacobi matrix; weak and strong convergence; cartesian currents; Sobolev space; approximation; smooth functions; nonlinear function spaces

UR - http://eudml.org/doc/247295

ER -

## References

top- 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. (1990) MR0980756
- Giaquinta M., Modica G., Souček J., Cartesian currents and variational problems for mappings into spheres, Annali S.N.S. Pisa 16 (1989), 393-485. (1989) MR1050333
- Giaquinta M., Modica G., Souček J., The Dirichlet energy of mappings with values into the sphere, Manuscripta Math. 65 (1989), 489-507. (1989) MR1019705
- Giaquinta M., Modica G., Souček J., The Dirichlet integral for mappings between manifolds: Cartesian currents and homology, Università di Firenze, preprint, 1991. MR1183409
- V. Šverák, Regularity properties of deformations with finite energy, Arch. Rat. Mech. Anal. 100 (1988), 105-127. (1988) MR0913960
- W.P. Ziemer, Weakly Differentiable Functions. Sobolev Spaces and Function of Bounded Variation, Graduate Text in Mathematics 120, Springer-Verlag, 1989. MR1014685

## Citations in EuDML Documents

top- Mariano Giaquinta, Giuseppe Modica, Jiří Souček, Some remarks about the $p$-Dirichlet integral
- Piotr Hajłasz, A note on weak approximation of minors
- Guido De Philippis, Weak notions of jacobian determinant and relaxation
- Guido De Philippis, Weak notions of Jacobian determinant and relaxation
- Irene Fonseca, Nicola Fusco, Paolo Marcellini, Topological degree, Jacobian determinants and relaxation

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.