A DIMENSION-REDUCING METHOD FOR THE POISSON EQUATION
Poisson 方程的一个降维算法

In this paper,the poisson equation with mixed boundary conditions is considered in a thinplate in R~3.By use of the asymptotic expansion,the three-dimensional problem is transformedinto two-dinensional solutions.The Sobolev in equality is further improved in the limiting cases.From this inequality,the maximum of the singular part of the asymptotic expansion of theequation is estimated.