论文标题
二级单调操作员的两尺度切割收敛
Two-scale cut-and-projection convergence for quasiperiodic monotone operators
论文作者
论文摘要
通过使用切割和投影方法将原始的准二级结构映射到更高维空间中的周期性结构中，可以将某些类别的Quasiperiodic单调算子进行定期均质化设置简化为周期性均质化设置。我们表征了非线性单调部分微分算子$ - \ mathrm {div} \; σ\left({\bf x},\frac{{\bf R}{\bf x}}η, \nabla u_η\right)$ for a bounded sequence $u_η$ in $W^{1,p}_0(Ω)$, where $1<p < \infty$, $Ω$ is a bounded open subset in $R^n$用Lipschitz边界。我们通过在高维空间中的超平面上定义的局部方程来确定均质的问题。建立了一个新的校正结果。
Averaging certain class of quasiperiodic monotone operators can be simplified to the periodic homogenization setting by mapping the original quasiperiodic structure onto a periodic structure in a higher dimensional space using cut-and projection method. We characterize cut-and-projection convergence limit of the nonlinear monotone partial differential operator $-\mathrm{div} \; σ\left({\bf x},\frac{{\bf R}{\bf x}}η, \nabla u_η\right)$ for a bounded sequence $u_η$ in $W^{1,p}_0(Ω)$, where $1<p < \infty$, $Ω$ is a bounded open subset in $R^n$ with Lipschitz boundary. We identify the homogenized problem with a local equation defined on the hyperplane in the higher-dimensional space. A new corrector result is established.
