k-quasiconvexity reduces to quasiconvexity

Cagnetti, Filippo (2011) k-quasiconvexity reduces to quasiconvexity. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 141 (4). pp. 673-708. ISSN 0308-2105

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Abstract

The relation between quasi-convexity and k-quasiconvexity (k greater than or equal to 2) is investigated. It is shown that every smooth strictly k-quasi-convex integrand with p-growth at infinity, p > 1, is the restriction to kth-order symmetric tensors of a quasiconvex function with the same growth. When the smoothness condition is dropped, it is possible to prove an approximation result. As a consequence, lower semicontinuity results for kth-order variational problems are deduced as corollaries of well-known first-order theorems. This generalizes a previous work by Dal Maso et al., in which the case where k = 2 was treated.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics
Depositing User: Filippo Cagnetti
Date Deposited: 20 Oct 2014 05:53
Last Modified: 16 Mar 2017 20:10
URI: http://sro.sussex.ac.uk/id/eprint/50644

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