Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-26T22:23:51.140Z Has data issue: false hasContentIssue false
  • English
  • Français

Lower semi-continuity for non-coercive polyconvex integrals in the limit case*

Part of: Existence theories Optimality conditions

Published online by Cambridge University Press:  10 December 2015

G. De Philippis ,
S. Di Marino  and
M. Focardi
G. De Philippis
Affiliation:
Hausdorff Center for Mathematics, Endenicher Allee 62, 53115 Bonn, Germany ([email protected])
S. Di Marino
Affiliation:
Scuola Normale Superiore di Pisa, Piazza dei Cavalieri 7, 56126 Pisa, Italy ([email protected])
M. Focardi
Affiliation:
Dipartimento di Matematica e Informatica ‘Ulisse Dini’, Università degli Studi di Firenze, Viale Morgagni 67/A, 50134 Firenze, Italy ([email protected])
Get access Rights & Permissions [Opens in a new window]

Extract

Lower semi-continuity results for polyconvex functionals of the calculus of variations along sequences of maps u: Ω ⊂ ℝn → ℝm in W1,m, 2 ⩽ m⩽ n, weakly converging in W1,m-1, are established. In addition, for m = n + 1, we also consider the autonomous case for weakly converging maps in W1,n-1.

Keywords

polyconvex integralsminorslower semi-continuity

MSC classification

Secondary: 49J45: Methods involving semicontinuity and convergence; relaxation 49K20: Problems involving partial differential equations
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 146 , Issue 2 , April 2016 , pp. 243 - 264
Copyright
Copyright © Royal Society of Edinburgh 2016 

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.)

Footnotes

*

In memory of Riccardo Ricci.

References

* In memory of Riccardo Ricci.