关于Green算子的Orlicz范数估计

Orlicz norm estimation for Green's operator

满足特定调和方程的微分形式的经典范数不等式在偏微分方程、位势分析以及工程技术领域有着广泛的应用.基于满足A-调和方程的微分形式的Ls-范数不等式,文中首先证明了有界域上作用于微分形式的Green算子的局部Orlicz范数估计,然后把上述结果推广到Lφ-平均域上,进而得到对应的全局的Orlicz范数估计.

Traditional norm inequalities of differential forms, which satisfy some certain kinds of harmonic equations, have been widely used in partial differential equations, potential analysis and engineering technology field. Based on L^s- norm inequality applying to differential forms which satisfy A-harmonic equation, it is proved that local Orlicz norm estimation for Green＇s operator can apply to differential forms on a convex bounded domain. Then the result is generalized to L^φ- averaging domains and the corresponding global Orlicz norm estimation is obtained.