二阶非线性椭圆型复方程的间断边值问题

Discontinuous Boundary Value Problem for Nonlinear Elliptic Complex Equations of Second Order

讨论了二阶非线性椭圆型方程在多连通区域上的间断边值问题。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的先验估计式,然后使用上述解的估计与Schauder不动点原理,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。

The article deals with the discontinuous boundary value problem for nonlinear elliptic complex equations of second order. Firstly, we bring up a modified boundary value problem, and give a priori estimates of it. Secondly, we use that estimates and Leray - Sehauder theorem to prove the existence of the solutions of this modified boundary value problem. Finally, we find out the condition in which the original problem can be solved.