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，我们研究定义在二维有界凸域内的标量通量作为积分辐射传输方程解的微分性质。基于 Vainikko 的正则定理，给出了在域边界附近标量通量导数的估计值。通过数值示例，展示了解的平滑性对钻石差分方法的收敛行为的影响。