Explicit Construction of Piecewise Affine Mappings with Constraints

• Autorzy: Waldemar Pompe
• Języki publikacji: EN

Abstrakty

EN

We construct explicitly piecewise affine mappings u:ℝ ⁿ → ℝ ⁿ 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.

Kategorie tematyczne

• 49K21: Problems involving relations other than differential equations
• 26B25: Convexity, generalizations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2010
• Tom: 58
• Numer: 3
• Strony: 209-220

Daty

wydano

2010

Twórcy

autor

Waldemar Pompe

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

Identyfikatory

DOI

10.4064/ba58-3-4