Homeomorphisms in the Sobolev space W1,n-1

被引：65

作者：

Csornyei, Marianna ^{[1
]}

Hencl, Stanislav ^{[2
]}

Maly, Jan ^{[2
,3
]}

机构：

[1] UCL, Dept Math, London WC1E 6BT, England

[2] Charles Univ Prague, Dept Math Anal, Prague 18600 8, Czech Republic

[3] Univ JE Purkyne, Dept Math, Usti Nad Labem 40096, Czech Republic

来源：

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK | 2010年 / 644卷

关键词：

FINITE DISTORTION; BOUNDED VARIATION; METRIC-SPACES; CONDITION-N; MAPPINGS; REGULARITY; INVERSE; INVERTIBILITY; VARIABLES;

D O I：

10.1515/CRELLE.2010.057

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let Omega subset of R-n be open. We show that each homeomorphism f is an element of W-loc(1,n-1)(Omega, R-n) satisfies f(-1) is an element of BVloc(f(Omega), R-n). If we moreover assume that f has finite distortion, then f(-1) is an element of W-loc(1,1)(f(Omega), R-n) and f(-1) has finite distortion. The main ingredient is a new result on change of variables in integral (area and coarea formula) for such mappings.

引用

页码：221 / 235

页数：15

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