Explicit Construction of Piecewise Affine Mappings with Constraints

Waldemar Pompe. "Explicit Construction of Piecewise Affine Mappings with Constraints." Bulletin of the Polish Academy of Sciences. Mathematics 58.3 (2010): 209-220. <http://eudml.org/doc/281268>.

@article{WaldemarPompe2010,
abstract = {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.},
author = {Waldemar Pompe},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
language = {eng},
number = {3},
pages = {209-220},
title = {Explicit Construction of Piecewise Affine Mappings with Constraints},
url = {http://eudml.org/doc/281268},
volume = {58},
year = {2010},
}

TY - JOUR
AU - Waldemar Pompe
TI - Explicit Construction of Piecewise Affine Mappings with Constraints
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2010
VL - 58
IS - 3
SP - 209
EP - 220
AB - 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.
LA - eng
UR - http://eudml.org/doc/281268
ER -