Explicit construction of piecewise affine mappings with constraints

• Autorzy: Pompe W.
• Języki publikacji: EN

Abstrakty

EN

We construct explicitly piecewise affine mappings u : Rn → Rn 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.

Słowa kluczowe

EN

rank-one convex hull; convex integration method; piecewise affine approximation of gradients

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2010
• Tom: Vol. 58, no 3
• Strony: 209--220
• Opis fizyczny: Bibliogr. 27 poz.

Twórcy

autor

Pompe W.

• Institute of Mathematics, Department of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland,

Bibliografia

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