Jacobians of Sobolev homeomorphisms

被引：32

作者：

Hencl, Stanislav ^{[1
]}

Maly, Jan ^{[1
,2
]}

机构：

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

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

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2010年 / 38卷 / 1-2期

关键词：

Sobolev mapping; Homeomorphism; Jacobian; Orientation;

D O I：

10.1007/s00526-009-0284-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let Omega subset of R(n) be a domain. We show that each homeomorphism f in the Sobolev space W(loc)(1,1) (Omega, R(n)) satisfies either J(f) >= 0 a.e or J(f) <= 0 a.e. if n = 2 or n = 3. For n > 3 we prove the same conclusion under the stronger assumption that f is an element of W(loc)(1,s) (Omega, R(n)) for some s > [n/2] (or in the setting of Lorentz spaces).

引用

页码：233 / 242

页数：10

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