Orientation-preserving Young measures

Koumatos, Konstantinos, Rindler, Filip and Wiedemann, Emil (2016) Orientation-preserving Young measures. Quarterly Journal of Mathematics, 67 (3). pp. 439-466. ISSN 0033-5606

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Abstract

We prove a characterization result in the spirit of the Kinderlehrer–Pedregal Theorem for Young measures generated by gradients of Sobolev maps satisfying the orientation-preserving constraint, that is, the pointwise Jacobian is positive almost everywhere. The argument to construct the appropriate generating sequences from such Young measures is based on a variant of convex integration in conjunction with an explicit lamination construction in matrix space. Our generating sequence is bounded in L^p for p less than the space dimension, a regime in which the pointwise Jacobian behaves flexibly, as is illustrated by our results. On the other hand, for p larger than or equal to the space dimension the situation necessarily becomes rigid and a construction as presented here cannot succeed. Applications to relaxation of integral functionals, the theory of semiconvex hulls and approximation of weakly orientation-preserving maps by strictly orientation-preserving ones in Sobolev spaces are given.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Analysis and Partial Differential Equations Research Group
Subjects: Q Science > QA Mathematics > QA0299 Analysis. Including analytical methods connected with physical problems
Depositing User: Konstantinos Koumatos
Date Deposited: 25 Jan 2017 12:04
Last Modified: 06 Jul 2017 20:42
URI: http://sro.sussex.ac.uk/id/eprint/66439

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