TY - JOUR
T1 - Deformations of finite conformal energy
T2 - Boundary behavior and limit theorems
AU - Iwaniec, Tadeusz
AU - Onninen, Jani
N1 - Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.
PY - 2011/11
Y1 - 2011/11
N2 - We study homeomorphisms h Y between two bounded domains in ℝn having finite conformal energy We consider the behavior of such mappings, including continuous extension to the closure of X and injectivity of h In general, passing to the weak W 1,n-limit of a sequence of homeomorphisms h one loses injectivity. However, if the mappings in question have uniformly bounded ℒ1-average of the inner distortion, then, for sufficiently regular domains X and Y, their limit map h: X Y is a homeomorphism. Moreover, the inverse map f=h-1: Y X enjoys finite conformal energy and has integrable inner distortion as well.
AB - We study homeomorphisms h Y between two bounded domains in ℝn having finite conformal energy We consider the behavior of such mappings, including continuous extension to the closure of X and injectivity of h In general, passing to the weak W 1,n-limit of a sequence of homeomorphisms h one loses injectivity. However, if the mappings in question have uniformly bounded ℒ1-average of the inner distortion, then, for sufficiently regular domains X and Y, their limit map h: X Y is a homeomorphism. Moreover, the inverse map f=h-1: Y X enjoys finite conformal energy and has integrable inner distortion as well.
KW - Boundary behavior of homeomorphisms
KW - Energy integrals
KW - Limit theorems
KW - Quasiconformal hyperelasticity
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U2 - 10.1090/S0002-9947-2011-05106-8
DO - 10.1090/S0002-9947-2011-05106-8
M3 - Article
AN - SCOPUS:79960776988
VL - 363
SP - 5605
EP - 5648
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
SN - 0002-9947
IS - 11
ER -