scholarly journals A new proof of gradient estimates for mean curvature equations with oblique boundary conditions

2016 ◽  
Vol 15 (5) ◽  
pp. 1719-1742 ◽  
Author(s):  
Jinju Xu
Keyword(s):  
Boundary Conditions ◽  
Mean Curvature ◽  
Gradient Estimates ◽  
Mean Curvature Equations ◽  
Oblique Boundary

Gradient Estimates for Spacelike Mean Curvature Flow with Boundary Conditions

2018 ◽  
Vol 62 (2) ◽  
pp. 459-469
Author(s):  
Ben Lambert
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Mean Curvature ◽  
Neumann Boundary Condition ◽  
Mean Curvature Flow ◽  
Neumann Boundary ◽  
Curvature Flow ◽  
Gradient Estimate ◽  
Gradient Estimates ◽  
The Mean

AbstractWe prove a gradient estimate for graphical spacelike mean curvature flow with a general Neumann boundary condition in dimension n = 2. This then implies that the mean curvature flow exists for all time and converges to a translating solution.

Gradient estimates of mean curvature equation with Neumann boundary condition in domains of Riemannian manifold

2017 ◽  
Vol 28 (08) ◽  
pp. 1750065
Author(s):  
Jinju Xu ◽  
Dekai Zhang
Keyword(s):  
Riemannian Manifold ◽  
Mean Curvature ◽  
Neumann Boundary Condition ◽  
Existence Result ◽  
Neumann Boundary ◽  
Gradient Estimates ◽  
The Maximum Principle ◽  
Curvature Equation ◽  
Mean Curvature Equation ◽  
Prescribed Mean Curvature Equation

We study the prescribed mean curvature equation with Neumann boundary conditions in domains of Riemannian manifold. The main goal is to establish the gradient estimates for solutions by the maximum principle. As a consequence, we obtain an existence result.

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