| Title:
|
Some remarks about the $p$-Dirichlet integral (English) |
| Author:
|
Giaquinta, Mariano |
| Author:
|
Modica, Giuseppe |
| Author:
|
Souček, Jiří |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
35 |
| Issue:
|
1 |
| Year:
|
1994 |
| Pages:
|
55-62 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We discuss variational problems for the $p$-Dirichlet integral, $p$ non integer, for maps between manifolds, illustrating the role played by the geometry of the target manifold in their weak formulation. (English) |
| Keyword:
|
variational problems |
| Keyword:
|
$p$--Dirichlet integral |
| MSC:
|
49J45 |
| MSC:
|
49Q20 |
| MSC:
|
58C99 |
| idZBL:
|
Zbl 0808.49038 |
| idMR:
|
MR1292583 |
| . |
| Date available:
|
2009-01-08T18:08:46Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118641 |
| . |
| Reference:
|
[1] Bethuel F.: The approximation problem for Sobolev maps between two manifolds.Acta Math. 167 (1992), 153-206. MR 1120602 |
| Reference:
|
[2] Bethuel F., Coron J., Demengel F., Helein F.: A cohomological criterion for density of smooth maps in Sobolev spaces between two manifolds.C.R.A.S., 1990. Zbl 0735.46017 |
| Reference:
|
[3] Brezis H., Coron J., Lieb E.: Harmonic maps with defects.Comm. Math. Phys. 107 (1986), 649-705. Zbl 0608.58016, MR 0868739 |
| Reference:
|
[4] Giaquinta M., Modica G., Souček J.: Calculus of Variations and Cartesian Currents.in preparation. |
| Reference:
|
[5] Giaquinta M., Modica G., Souček J.: Cartesian currents and variational problems for mappings into spheres.Ann. Sc. Norm. Sup. Pisa 16 (1989), 393-485. MR 1050333 |
| Reference:
|
[6] Giaquinta M., Modica G., Souček J.: Cartesian currents, weak diffeomorphisms and existence theorems in nonlinear elasticity.Arch. Rat. Mech. Anal. 106 (1989), 97-159 Erratum and addendum Arch. Rat. Mech. Anal. 109 (1990, 385-392). MR 0980756 |
| Reference:
|
[7] 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:
|
[8] Giaquinta M., Modica G., Souček J.: The Dirichlet integral for mappings between manifolds: Cartesian currents and homology.Math. Ann. 294 (1992), 325-386. MR 1183409 |
| Reference:
|
[9] Giaquinta M., Modica G., Souček J.: The gap phenomenon for variational integrals in Sobolev spaces.Proc. Roy. Soc. Edinburg 120 (1992), 93-98. MR 1149986 |
| Reference:
|
[10] Hardt R., Lin F.: A remark on $H^1$ mappings.Manuscripta Math. 56 (1986), p. 1010. MR 0846982 |
| Reference:
|
[11] Malý J.: $L^p$-approximation of Jacobians.Comment. Math. Univ. Carolinae 32 (1991), 659-666. MR 1159812 |
| . |
