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域上的标量通量作为积分辐射传输方程解的微分性质。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。