一类具有转向点超曲面的奇摄动椭圆型方程边值问题

讨论了n维空间中如下一类具有转向点超曲面的奇摄动椭圆型方程的边值问题Lεu≡εLu ∑^ni=1fi(x1,……,xn)Эu/Эxi g(x1,……,xn)u=0,(x1,……,xn)∈Ω，u（x1,……，xn)│ЭΩ1=φ1(x1,……,xn-1),ai≤xi≤bi,u(x1,……,xn)│ЭΩ2=φ2(x1,……,xn-1),ai≤xi≤bi。其中：ε为一正参数，且L=∑ni,j=1aij(x1,……,xn)Э^2/ЭxiЭxj(aij=aji),∑ni,j=1aijξiξj≥λ∑ni=1ξ^2i,任意ξi∈R,i=1,2,……,n,λ＞0。利用多重尺度法和比较定理、就形坐标和抛物柱函数，研究了该边值问题解的渐近性态。

A Class of Elliptic Equation Boundary Value Problems with a Super Surface of Turning Point in n-dimensional Space

A class of singularly perturbed elliptic equation boundary value problems with a super surface of turning point in n-dimensional space is considered in the following Lεu≡εLu+∑ni=1fi(x1,…，xn)(u)/(xi)+g(x1,…，xn)u=0, (x1,…,xn)∈Ω， u(x1,…,xn)｜Ω1=Φ1(x1,…，xn-1),　ai≤xi≤bi， u(x1,…,xn)｜Ω2=Φ2(x1,…,xn-1),　ai≤xi≤bi. where ε is a positive parameter and L=∑ni,j=1aij(x1,…,xn)(2)/(xixj)　(aij=aji)， ∑ni,j=1aijξiξj≥λ∑ni=1ξ2i, ξi∈R,i=1,2,…,n,λ＞0. By using the method of multiple scales and the comparison theorem, by introducing the strained coordinate and the parabolic cylinder functions, the asymptotic behavior of solution for the boundary value problem is studied.