通过层的低秩梯度Sobolev同胚
Sobolev homeomorphisms with gradients of low rank via laminates
摘要：
设$Ω\subset \mathbb{R}^{n}$是有界开集.给定$2\leq m\leq n$，构造一个凸函数$ϕ:Ω\to \mathbb{R}$，其梯度$f= \nabla ϕ$是Hölder连续同胚，$f$是$\partial Ω$上的恒等式，其导数$D f$的秩为$m-1$ a.e.在$Ω$和$D f$中，在弱$L^{m}$空间$L^{m,w}$中。证明是基于凸积分和阶梯层压板。
英文摘要：
Let $Ω\subset \mathbb{R}^{n}$ be a bounded open set. Given $2\leq m\leq n$, we construct a convex function $ϕ:Ω\to \mathbb{R}$ whose gradient $f= \nabla ϕ$ is a Hölder continuous homeomorphism, $f$ is the identity on $\partial Ω$, the derivative $D f$ has rank $m-1$ a.e.\ in $Ω$ and $D f$ is in the weak $L^{m}$ space $L^{m,w}$. The proof is based on convex integration and staircase laminates.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
