单稳型拟线性椭圆问题的重合集
Coincidence sets in quasilinear elliptic problems of monostable type
摘要：
本文讨论单稳型$p$ -Laplacian椭圆问题正解的重合集的形成.证明了对于扩散项的任意小参数，如果$a(x)$是$p$ -调和函数（但不是常数）且零点的阶数小于1，则解与反应项在开集的稳定零函数$a(x)$重合.因此，它也表明，该解决方案是小于$a(x)$，如果$a(x)$是一个零阶大于或等于1。证明依赖于比较定理和能量方法获得局部比较函数。
英文摘要：
This paper concerns the formation of a coincidence set for the positive solution of $p$-Laplacian elliptic problems of monostable type. It is proved that for any small parameter of diffusion term, the solution coincides with the stable zero-function $a(x)$ of reaction term in an open set if $a(x)$ is $p$-harmonic (but, not constant) and a zero of order less than 1. Inversely, it is also shown that the solution is less than $a(x)$ if $a(x)$ is a zero of order greater than or equal to 1. The proof rely on comparison theorems and an energy method for obtaining local comaprison functions.
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