We consider a fourth order, reaction-diffusion type, singularly perturbed boundary value problem, and the regularity of its solution. Specifically, we provide estimates for arbitrary order derivatves, which are explicit in the singular perturbation parameter as well as the differentiation order. Such estimates are needed for the numerical analysis of high order methods, e.g.hp Finite Element Method (FEM).

翻译：本文研究一个四阶反应扩散型奇异摄动边值问题及其解的正则性。具体而言，我们提供了任意阶导数的估计，这些估计显式依赖于奇异摄动参数和求导阶数。此类估计对于高阶方法（如hp有限元法）的数值分析是必要的。