| Title:
|
$L^p$-approximation of Jacobians (English) |
| Author:
|
Malý, Jan |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
32 |
| Issue:
|
4 |
| Year:
|
1991 |
| Pages:
|
659-666 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $q<p$. An example is shown of a function which is in $\operatorname{cart}^p(\Omega ,\bold R^2)$ but not in $\operatorname{cart}^p(\Omega ,\bold R^2)$. (English) |
| Keyword:
|
Sobolev spaces |
| Keyword:
|
minors of the Jacobi matrix |
| Keyword:
|
weak and strong convergence |
| Keyword:
|
cartesian currents |
| MSC:
|
28A75 |
| MSC:
|
46E40 |
| MSC:
|
49J45 |
| MSC:
|
73C50 |
| MSC:
|
74B20 |
| idZBL:
|
Zbl 0753.46024 |
| idMR:
|
MR1159812 |
| . |
| Date available:
|
2009-01-08T17:47:56Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118445 |
| . |
| Reference:
|
[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 0980756 |
| Reference:
|
[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 1050333 |
| Reference:
|
[3] Giaquinta M., Modica G., Souček J.: The Dirichlet energy of mappings with values into the sphere.Manuscripta Math. 65 (1989), 489-507. MR 1019705 |
| Reference:
|
[4] Giaquinta M., Modica G., Souček J.: The Dirichlet integral for mappings between manifolds: Cartesian currents and homology.Università di Firenze, preprint, 1991. MR 1183409 |
| Reference:
|
[5] V. Šverák: Regularity properties of deformations with finite energy.Arch. Rat. Mech. Anal. 100 (1988), 105-127. MR 0913960 |
| Reference:
|
[6] W.P. Ziemer: Weakly Differentiable Functions. Sobolev Spaces and Function of Bounded Variation.Graduate Text in Mathematics 120, Springer-Verlag, 1989. MR 1014685 |
| . |
