论文标题
对于光滑内核的非局部问题的均质化
Homogenization for nonlocal problems with smooth kernels
论文作者
论文摘要
在本文中，我们考虑了涉及不同光滑内核的非局部方程的均质化问题。 We assume that the spacial domain is divided into a sequence of two subdomains $A_n \cup B_n$ and we have three different smooth kernels, one that controls the jumps from $A_n$ to $A_n$, a second one that controls the jumps from $B_n$ to $B_n$ and the third one that governs the interactions between $A_n$ and $B_n$. Assuming that $χ_{A_n} (x) \to X(x)$ weakly-* in $L^\infty$ (and then $χ_{B_n} (x) \to (1-X)(x)$ weakly-* in $L^\infty$) as $n \to \infty$ we show that there is an homogenized limit system in which the three kernels and the limit function $X$ 出现。 我们处理Neumann和Dirichlet边界条件。此外，我们还提供了对结果的概率解释。
In this paper we consider the homogenization problem for a nonlocal equation that involve different smooth kernels. We assume that the spacial domain is divided into a sequence of two subdomains $A_n \cup B_n$ and we have three different smooth kernels, one that controls the jumps from $A_n$ to $A_n$, a second one that controls the jumps from $B_n$ to $B_n$ and the third one that governs the interactions between $A_n$ and $B_n$. Assuming that $χ_{A_n} (x) \to X(x)$ weakly-* in $L^\infty$ (and then $χ_{B_n} (x) \to (1-X)(x)$ weakly-* in $L^\infty$) as $n \to \infty$ we show that there is an homogenized limit system in which the three kernels and the limit function $X$ appear. We deal with both Neumann and Dirichlet boundary conditions. Moreover, we also provide a probabilistic interpretation of our results.
