论文标题
$γ$ - 在$ \ mathbb {r}^n $的有限子集中的某些非本地周围的$ convergence带有一般边界条件
$Γ$-convergence of some nonlocal perimeters in bounded subsets of $\mathbb{R}^n$ with general boundary conditions
论文作者
论文摘要
我们建立了一些能量功能的$γ$ - 融合，这些功能描述了有限域中的非本地吸引人相互作用。相互作用的电势求解了有限域中的椭圆方程（局部或非局部性），我们结果的主要兴趣是确定施加的边界条件对限制功能的影响。我们将一般的罗宾边界条件考虑在内，其中包括Dirichlet和Neumann条件为特定情况。根据椭圆运算符的顺序，极限功能涉及通常的周长或某些分数周边。 我们还考虑了相关能量功能的$γ$ - 结合了通常的周长功能和非本地排斥相互作用能量。
We establish the $Γ$-convergence of some energy functionals describing nonlocal attractive interactions in bounded domains. The interaction potential solves an elliptic equation (local or nonlocal) in the bounded domain and the primary interest of our results is to identify the effects that the boundary conditions imposed on the potential have on the limiting functional. We consider general Robin boundary conditions, which include Dirichlet and Neumann conditions as particular cases. Depending on the order of the elliptic operator the limiting functional involves the usual perimeter or some fractional perimeter. We also consider the $Γ$-convergence of a related energy functional combining the usual perimeter functional and the nonlocal repulsive interaction energy.
