论文标题
部分可观测时空混沌系统的无模型预测
Weak limit of homeomorphisms in $W^{1,n-1}$: invertibility and lower semicontinuity of energy
论文作者
论文摘要
令$ω$，$ω'\ subset \ mathbb {r}^n $为有界域，让$ f_m \colonΩ\toΩ'$是一系列同构型同构，jacobians $ j_ {f_m}> 0 $a。并规定了Dirichlet边界数据。让所有$ f_m $ $满足lusin（n）条件和$ \ sup_m \int_Ω（| df_m | |^{n-1}+a（| \ text {cof} df_m |）+ϕ（j_f））<\ infty $，其中$ a $ a $ a $ a $ a $ a $ a $ and $φ$ as as as as as asure Convex函数。令$ f $是$ w^{1，n-1} $的$ f_m $的弱极限。如果$ a $ a和$φ$的某些增长行为，我们表明$ f $满足conti和de lellis的（INV）条件，lusin（n）条件（n）条件和polyconvex Energies是较低的半连续性。
Let $Ω$, $Ω'\subset\mathbb{R}^n$ be bounded domains and let $f_m\colonΩ\toΩ'$ be a sequence of homeomorphisms with positive Jacobians $J_{f_m} >0$ a.e. and prescribed Dirichlet boundary data. Let all $f_m$ satisfy the Lusin (N) condition and $\sup_m \int_Ω(|Df_m|^{n-1}+A(|\text{cof} Df_m|)+ϕ(J_f))<\infty$, where $A$ and $φ$ are positive convex functions. Let $f$ be a weak limit of $f_m$ in $W^{1,n-1}$. Provided certain growth behaviour of $A$ and $φ$, we show that $f$ satisfies the (INV) condition of Conti and De Lellis, the Lusin (N) condition, and polyconvex energies are lower semicontinuous.
