二阶椭圆型方程在多连通区域上的一些间断边值问题

Some Discontinuous Boundary Value Problems for Nominear Elliptic Equations of Second Order in Multiply Connected Plane Domains

主要讨论二阶非线性椭圆型方程在多连通区域上的间断Ｐｏｉｎｃａｒｅ’边值问题。这里，我们先提出此边值问题的一种新的适定提法，并给出这种变态边值问题解的先验估计式，然后使用上述解的估计与Ｓｃｈａｕｄｅｒ不动点定理，证明这种变态边值问题解的存在性，进而导出原边值问题的可解条件。

In this paper,we mainly discuss the discontinuous Poineare’boundary value problem for non-linear elliptic equations of second order in multiply connected doinains.Firstly ,we give a new well-posedness of the Poincare'problem and obtain a priorlestimates of solutions for the modified prob-em. Secondly,by using the above estimates of solutions and the Schauder fixed-point theorem,weprove the solvability of the above medified problem,moreover,the solvability conditions of the o-riginal Poincare'problem are derived.