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：我们考虑一个四阶、反应扩散型、奇异摄动边值问题及其解的解析正则性。具体而言，我们给出了任意阶导数的估计，这些估计显式地依赖于奇异摄动参数以及求导阶数。此类估计对高阶方法（例如hp有限元方法（FEM））的数值分析是必需的。