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Explicit Construction of Piecewise Affine Mappings with Constraints by Waldemar POMPE
| Content Provider | Semantic Scholar |
|---|---|
| Author | Pompe, Waldemar Bojarski, Bogdan |
| Copyright Year | 2011 |
| Abstract | We construct explicitly piecewise affine mappings u : R → R with affine boundary data satisfying the constraint div u = 0. As an application of the construction we give short and direct proofs of the main approximation lemmas with constraints in convex integration theory. Our approach provides direct proofs avoiding approximation by smooth mappings and works in all dimensions n ≥ 2. After a slight modification of our construction, the constraint div u = 0 can be turned into det Du = 1, giving new examples of piecewise affine mappings u with det Du = 1. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://www.impan.pl/shop/publication/transaction/download/product/85713 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |