A convexity problem for a semi-linear PDE

被引：2
作者：
El Hajj, Layan [1 ]
机构：
[1] Amer Univ Dubai, Dubai, U Arab Emirates
来源：
APPLICABLE ANALYSIS | 2021年 / 100卷 / 08期
关键词：
Convexity; star-shapedness; uniqueness; free boundary; FREE-BOUNDARY; LEVEL SETS;
D O I：
10.1080/00036811.2019.1667981
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we prove convexity of super-level sets of a semi-linear PDE with a non-monotone right-hand side, and with a free boundary Delta u = chi{0<u<1} in R-n\D, u = 2 on partial derivative D. (1) Here D is assumed to be convex, and n >= 2. The main difficulty of this problem is that the right-hand side is non-monotone and no a-priori regularity is known about the boundary partial derivative{u > 0}.
引用
收藏
页码：1816 / 1826
页数：11
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