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

Part of: Optimality conditions Existence theories

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])
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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 

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Footnotes

*

In memory of Riccardo Ricci.

References

* In memory of Riccardo Ricci.