Some remarks about the p -Dirichlet integral

Mariano Giaquinta; Giuseppe Modica; Jiří Souček

Commentationes Mathematicae Universitatis Carolinae (1994)

  • Volume: 35, Issue: 1, page 55-62
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Giaquinta, Mariano, Modica, Giuseppe, and Souček, Jiří. "Some remarks about the $p$-Dirichlet integral." Commentationes Mathematicae Universitatis Carolinae 35.1 (1994): 55-62. <http://eudml.org/doc/247642>.

@article{Giaquinta1994,
abstract = {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.},
author = {Giaquinta, Mariano, Modica, Giuseppe, Souček, Jiří},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {variational problems; $p$–Dirichlet integral; concentrations; -Dirichlet integral; compact Riemannian manifolds; variational problem; Sobolev spaces},
language = {eng},
number = {1},
pages = {55-62},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Some remarks about the $p$-Dirichlet integral},
url = {http://eudml.org/doc/247642},
volume = {35},
year = {1994},
}

TY - JOUR
AU - Giaquinta, Mariano
AU - Modica, Giuseppe
AU - Souček, Jiří
TI - Some remarks about the $p$-Dirichlet integral
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1994
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 35
IS - 1
SP - 55
EP - 62
AB - 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.
LA - eng
KW - variational problems; $p$–Dirichlet integral; concentrations; -Dirichlet integral; compact Riemannian manifolds; variational problem; Sobolev spaces
UR - http://eudml.org/doc/247642
ER -

References

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  1. Bethuel F., The approximation problem for Sobolev maps between two manifolds, Acta Math. 167 (1992), 153-206. (1992) MR1120602
  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. Zbl0735.46017
  3. Brezis H., Coron J., Lieb E., Harmonic maps with defects, Comm. Math. Phys. 107 (1986), 649-705. (1986) Zbl0608.58016MR0868739
  4. Giaquinta M., Modica G., Souček J., Calculus of Variations and Cartesian Currents, in preparation. 
  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. (1989) MR1050333
  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). (1990, 385-392) MR0980756
  7. Giaquinta M., Modica G., Souček J., The Dirichlet energy of mappings with values into the sphere, Manuscripta Math. 65 (1989), 489-507. (1989) MR1019705
  8. Giaquinta M., Modica G., Souček J., The Dirichlet integral for mappings between manifolds: Cartesian currents and homology, Math. Ann. 294 (1992), 325-386. (1992) MR1183409
  9. Giaquinta M., Modica G., Souček J., The gap phenomenon for variational integrals in Sobolev spaces, Proc. Roy. Soc. Edinburg 120 (1992), 93-98. (1992) MR1149986
  10. Hardt R., Lin F., A remark on H 1 mappings, Manuscripta Math. 56 (1986), p. 1010. (1986) MR0846982
  11. Malý J., L p -approximation of Jacobians, Comment. Math. Univ. Carolinae 32 (1991), 659-666. (1991) MR1159812

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