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k-quasiconvexity reduces to quasiconvexity
journal contribution
posted on 2023-06-08, 18:44 authored by Filippo CagnettiThe 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.
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Publication status
- Published
File Version
- Accepted version
Journal
Proceedings of the Royal Society of Edinburgh: Section A MathematicsISSN
0308-2105Publisher
Cambridge University PressExternal DOI
Issue
4Volume
141Page range
673-708Department affiliated with
- Mathematics Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2014-10-20First Open Access (FOA) Date
2014-10-20First Compliant Deposit (FCD) Date
2014-10-18Usage metrics
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