In this paper, we deal with the differential properties of the scalar flux defined over a two-dimensional bounded convex domain, as a solution to the integral radiation transfer equation. Estimates for the derivatives of the scalar flux near the boundary of the domain are given based on Vainikko's regularity theorem. A numerical example is presented to demonstrate the implication of the solution smoothness on the convergence behavior of the diamond difference method.

翻译：在本文中，我们研究了定义在二维有界凸域上的标量通量的微分特性，作为积分辐射转移方程的解。基于Vainikko的正则性定理，给出了标量通量在域边界附近的导数估计。通过数值实例说明了解的平滑性对于钻石差分方法的收敛行为的影响。