论文标题
关于椭圆形和抛物线方程的Neumann问题
On Neumann problems for elliptic and parabolic equations on bounded manifolds
论文作者
论文摘要
在本文中，我们研究了具有光滑边界的紧凑型riemannian歧管上的Neumann边界条件的完全非线性二阶椭圆方程和抛物线方程。假设存在合适的$ \ Mathcal {c} $ -Subsolutions，我们为具有Neumann边界条件的可允许解决方案提供了振荡界限。我们使用一种抛物线方法来得出$ K $ -Hessian方程，并在适当的假设下$u_ν= ϕ（x）$。
In this paper, we study fully nonlinear second-order elliptic and parabolic equations with Neumann boundary conditions on compact Riemannian manifolds with smooth boundary. We derive oscillation bounds for admissible solutions with Neumann boundary condition $u_ν= ϕ(x)$ assuming the existence of suitable $\mathcal{C}$-subsolutions. We use a parabolic approach to derive a solution of a $k$-Hessian equation with Neumann boundary condition $u_ν= ϕ(x)$ under suitable assumptions.
