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：本文研究定义在二维有界凸区域上的标量通量的微分性质，作为积分辐射传输方程的解。基于Vainikko正则性定理，给出了标量通量在区域边界附近导数的估计。通过数值算例展示了解的光滑性对菱形差分法收敛行为的影响。