TY - JOUR
T1 - Mappings of finite distortion
T2 - Compactness
AU - Iwaniec, Tadeusz
AU - Koskela, Pekka
AU - Onninen, Jani
PY - 2002
Y1 - 2002
N2 - We study mappings f: Ω ↠ Rn whose distortion functions Kl(x,f), l = 1, 2, . . . , n - 1, are in general unbounded but subexponentially integrable. The main result is the weak compactness principle. It asserts that a family of mappings with prescribed volume integral ∫ Ω J(x, f) dx, and with given subexponential norm ∥1√Kl∥ExpA of a distortion function, is closed under weak convergence. The novelty of this result is twofold. Firstly, it requires integral bounds on the distortions Kl(x, f) which are weaker than those for the usual outer distortion. Secondly, the category of subexponential bounds is optimal to fully describe the compactness principle for mappings of unbounded distortion, even when outer distortion is used.
AB - We study mappings f: Ω ↠ Rn whose distortion functions Kl(x,f), l = 1, 2, . . . , n - 1, are in general unbounded but subexponentially integrable. The main result is the weak compactness principle. It asserts that a family of mappings with prescribed volume integral ∫ Ω J(x, f) dx, and with given subexponential norm ∥1√Kl∥ExpA of a distortion function, is closed under weak convergence. The novelty of this result is twofold. Firstly, it requires integral bounds on the distortions Kl(x, f) which are weaker than those for the usual outer distortion. Secondly, the category of subexponential bounds is optimal to fully describe the compactness principle for mappings of unbounded distortion, even when outer distortion is used.
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M3 - Article
AN - SCOPUS:0036457983
SN - 1239-629X
VL - 27
SP - 391
EP - 417
JO - Annales Academiae Scientiarum Fennicae Mathematica
JF - Annales Academiae Scientiarum Fennicae Mathematica
IS - 2
ER -