Orientation-preserving Young measures
journal contribution
posted on 2023-06-09, 04:55 authored by Konstantinos KoumatosKonstantinos Koumatos, Filip Rindler, Emil WiedemannWe 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.
History
Publication status
- Published
File Version
- Accepted version
Journal
Quarterly Journal of MathematicsISSN
0033-5606Publisher
Oxford University PressExternal DOI
Issue
3Volume
67Page range
439-466Department affiliated with
- Mathematics Publications
Research groups affiliated with
- Analysis and Partial Differential Equations Research Group Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2017-01-25First Open Access (FOA) Date
2017-07-01First Compliant Deposit (FCD) Date
2017-01-24Usage metrics
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