Local invertibility of Sobolev functions
Local invertibility of Sobolev functions
复制标题
Sobolev 函数的局部可逆性
DOI：
10.1137/s0036141093257416
复制
发表时间：
1995
影响因子：
2
通讯作者：
W. Gangbo
中科院分区：
文献类型：
--
作者：
I. Fonseca;W. Gangbo
A local inverse function theorem is established for mappings $v \in W^{1,N} (\Omega ,\mathbb{R}^N )$, $\Omega \subset \mathbb{R}^N $ open set, such that $\det \nabla v(x) > 0$ almost everywhere in $x \in \Omega $. Regularity of the local inverse $v^{ - 1} $ is obtained provided that $| {\frac{{{\text{adj}}(\nabla v)}}{{\det \nabla v}}} |^s \det \nabla v \in L^1 (\Omega )$ for some $1 \leq s < + \infty $. The local invertibility property is used to study the weak lower semicontinuity of a functional involving variation of the domain.
A local inverse function theorem is established for mappings $v \in W^{1,N} (\Omega ,\mathbb{R}^N )$, $\Omega \subset \mathbb{R}^N $ open set, such that $\det \nabla v(x) > 0$ almost everywhere in $x \in \Omega $. Regularity of the local inverse $v^{ - 1} $ is obtained provided that $| {\frac{{{\text{adj}}(\nabla v)}}{{\det \nabla v}}} |^s \det \nabla v \in L^1 (\Omega )$ for some $1 \leq s < + \infty $. The local invertibility property is used to study the weak lower semicontinuity of a functional involving variation of the domain.