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polyconvex integrals

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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1 results

Lower semi-continuity for non-coercive polyconvex integrals in the limit case *
Part of
- Existence theories
- Optimality conditions
G. De Philippis, S. Di Marino, M. Focardi
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 146 / Issue 2 / April 2016

Published online by Cambridge University Press:

10 December 2015, pp. 243-264

Print publication:

April 2016
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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.