一类双调和方程的可解性

在洞型区域内研究边界值问题可追溯到Lions的工作,在那里他在考虑地质学一个问题时,在一个洞型区内分别给出了内外边界值,最近几年,双调和方程问题的研究一直比较活跃,但在洞型区域内对此问题的研究尚未见到。该文将双调和方程问题化为椭圆方程组问题,利用上、下解方法以及极值原理、嵌入定理和Leray-Schauder不动点定理证明了在洞型区域内一类双调和方程边值问题弱解的存在性定理。

Solvability of a class of biharmonic equation

Studying the boundary value problem on a domain with a hole can be traced back to Lions' work,in which he gave the inner and outer boundary of domain respectively when he considered a geological problem. In recent years,researchers have been interested in the study of the boundary value problem while the biharmonic equation is considered, but on a domain with a hole, the study of biharmonic equation has not been seen. In this paper,the biharmonic equation problem is transformed into the elliptic equation system problem,and an existence theorem of weak solution to the problem of a class of biharmonic equation is proved by utilizing the sub-supersolution method, the extreme value principle,the embedding theorem and Leray-Schauder fixed point theorem.