Hostname: page-component-77c89778f8-m42fx Total loading time: 0 Render date: 2024-07-24T22:24:24.325Z Has data issue: false hasContentIssue false
  • English
  • Français

The gap phenomenon for variational integrals in Sobolev spaces*

Published online by Cambridge University Press:  14 November 2011

M. Giaquinta ,
G. Modica  and
J. Souček
M. Giaquinta
Affiliation:
Dip. di Matematica Applicata, Università di Firenze, Via S. Marta, 3, I-50139 Firenze, Italy
G. Modica
Affiliation:
Dip. di Matematica Applicata, Università di Firenze, Via S. Marta, 3, I-50139 Firenze, Italy
J. Souček
Affiliation:
Československá Akademie Věd, Matematický Ústav, Žitná, 25, 11567 Praha, Czechoslovakia
Get access Rights & Permissions [Opens in a new window]

Synopsis

We show that a gap phenomenon occurs for general variational integrals for mappings from a domain Rn into a Riemannian manifold if has a non-trivial topology.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 120 , Issue 1-2 , 1992 , pp. 93 - 98
Copyright
Copyright © Royal Society of Edinburgh 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Bethuel, F.. The approximation problem for Sobolev maps between two manifolds (preprint).Google Scholar
2Brezis, H.. Sk-valued maps with singilarities. In Topics in Calculus of Variations, Ed. Giaquinta, M., Lecture Notes in Mathematics 1365 (Berlin: Springer, 1989).Google Scholar
3Federer, H.. Geometric measure theory (New York: Springer, 1969).Google Scholar
4Federer, H. and Fleming, W.. Normal and integral currents. Ann. of Math. 72 (1960), 458–520.CrossRefGoogle Scholar
5Giaquinta, M., Modica, G. and Souček, J.. Cartesian currents and variational problems for mappings into spheres. Ann. Scuola Norm. Sup. Pisa 16 (1989), 393–485.Google Scholar
6Giaquinta, M., Modica, G. and Souček, J.. The Dirichlet integral for mappings between manifolds: cartesian currents and homology (preprint).Google Scholar
7Hardt, R. and Lin, F. H.. A remark on H1 mappings. Manuscripta Math. 56 (1986), 1010.CrossRefGoogle Scholar
8Simon, L.. Lectures on geometric measure theory, Proc. of the Centre for Math. Analysis 3 (Canberra: Australian National University, 1983).Google Scholar