TY - JOUR
T1 - Triangulation of diffeomorphisms
AU - Iwaniec, Tadeusz
AU - Onninen, Jani Kristian
PY - 2016/5/23
Y1 - 2016/5/23
N2 - Is it possible to approximate a diffeomorphism of Euclidean domains with piecewise affine homeomorphisms, locally uniformly up to the first order derivatives? The answer is yes. However, any effort to provide a rigorous and clear proof reveals the complexity of this question, especially in higher dimensions. It is the objective of the present paper to formulate this question in its greatest generality, as well as to provide all details for the affirmative answer, Theorem 1.1. A novelty, which has broader applications, is the construction of selfsimilar isotropic triangulation of the Euclidean domains, Theorem 1.2.
AB - Is it possible to approximate a diffeomorphism of Euclidean domains with piecewise affine homeomorphisms, locally uniformly up to the first order derivatives? The answer is yes. However, any effort to provide a rigorous and clear proof reveals the complexity of this question, especially in higher dimensions. It is the objective of the present paper to formulate this question in its greatest generality, as well as to provide all details for the affirmative answer, Theorem 1.1. A novelty, which has broader applications, is the construction of selfsimilar isotropic triangulation of the Euclidean domains, Theorem 1.2.
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U2 - 10.1007/s00208-016-1426-x
DO - 10.1007/s00208-016-1426-x
M3 - Article
AN - SCOPUS:84969808334
SP - 1
EP - 37
JO - Mathematische Annalen
JF - Mathematische Annalen
SN - 0025-5831
ER -