Gradient estimates for semilinear elliptic systems and other related results

被引:10
|
作者
Smyrnelis, Panayotis [1 ]
机构
[1] Univ Athens, Dept Math, Athens 15784, Greece
关键词
Modica's estimate; Liouville theorem; gradient estimates; entire solutions to elliptic systems; stress-energy tensor; monotonicity formula;
D O I
10.1017/S0308210515000347
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
A periodic connection is constructed for a double well potential defined in the plane. This solution violates Modica's estimate as well as the corresponding Liouville theorem for general phase transition potentials. Gradient estimates are also established for several kinds of elliptic systems. They allow us to prove the Liouville theorem in some particular cases. Finally, we give an alternative form of the stress-energy tensor for solutions defined in planar domains. As an application, we deduce a (strong) monotonicity formula.
引用
收藏
页码:1313 / 1330
页数:18
相关论文
共 50 条