SOME MAXIMUM PRINCIPLES AND SYMMETRY RESULTS FOR A CLASS OF BOUNDARY VALUE PROBLEMS INVOLVING THE MONGE-AMPÈRE EQUATION
SOME MAXIMUM PRINCIPLES AND SYMMETRY RESULTS FOR A CLASS OF BOUNDARY VALUE PROBLEMS INVOLVING THE MONGE-AMPÈRE EQUATION
复制标题
一类涉及蒙日-安培方程边值问题的极大值原理及对称性结果
DOI：
10.1142/s0218202501001240
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发表时间：
2001
影响因子：
3.5
通讯作者：
A. Safoui
中科院分区：
文献类型：
--
作者：
G. Philippin;A. Safoui
本文研究了一类Monge-Ampere方程的边值问题，其中Ω是RN中的严格凸有界区域，N≥2.当f=g（u）h（|u| 2）与g和h满足微分不等式，我们显示在Sec. 2，函数在边界上取最大值。这个最大值原理推广了马云最近的一个结果，他研究了R2中f=const的情况。节中3.在特定的边界条件或Ω的几何条件下，研究了u的对称性。
In this paper we investigate a class of boundary value problems for the Monge-Ampere equation where Ω is a strictly convex bounded domain in RN, N≥2. When f=g(u)h(|∇u|2) with g and h satisfying the differential inequality we show in Sec. 2 that the function takes its maximum value on the boundary ∂Ω. This maximum principle generalizes a recent result of Ma who investigated the case f=const in R2. In Sec. 3 we investigate symmetry properties of u under specific boundary conditions or geometry of Ω.