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,我们讨论作为整体辐射转移方程式的解决方案,在两维结合的锥形上界定的二次曲线通量的差别性。根据Vainikko的规律性理论,给出了该区域边界附近天际通量衍生物的估算值。我们举了一个数字例子,以证明解决方案的平稳性对钻石差异法的趋同行为的影响。