论文标题
关于Riemannian歧管上完全非线性方程的强大最大原理的注释
A note on the strong maximum principle for fully nonlinear equations on Riemannian manifolds
论文作者
论文摘要
我们研究了不完全退化且满足适当缩放条件的Riemannian流形的完全非线性二阶方程的强大最大（和最小）原理。我们的结果适用于大型的非线性操作员，其中Pucci的极端操作员，一些奇异的操作员，例如以$ p $ - $ \ infty $ -laplacian建模的运算符，以及平均曲率类型问题。作为副产品，当歧管具有非负分段曲率时，我们为某些二阶均匀椭圆问题建立了新的强比较原理。
We investigate strong maximum (and minimum) principles for fully nonlinear second order equations on Riemannian manifolds that are non-totally degenerate and satisfy appropriate scaling conditions. Our results apply to a large class of nonlinear operators, among which Pucci's extremal operators, some singular operators like those modeled on the $p$- and $\infty$-Laplacian, and mean curvature type problems. As a byproduct, we establish new strong comparison principles for some second order uniformly elliptic problems when the manifold has nonnegative sectional curvature.
