scholarly journals Hessian estimates for Lagrangian mean curvature equation

2021 ◽  
Vol 60 (6) ◽  
Author(s):  
Arunima Bhattacharya
Keyword(s):  
Mean Curvature ◽  
Curvature Equation ◽  
Mean Curvature Equation ◽  
Hessian Estimates

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.

A generalization of the asymptotic behavior of Palais-Smale sequences on a manifold with boundary

2018 ◽  
Vol 29 (10) ◽  
pp. 1850069
Author(s):  
Hong Zhang
Keyword(s):  
Asymptotic Behavior ◽  
Boundary Value Problem ◽  
Mean Curvature ◽  
Compact Manifold ◽  
Boundary Value ◽  
Fundamental Solutions ◽  
Curvature Equation ◽  
Mean Curvature Equation ◽  
Manifold With Boundary ◽  
Prescribed Mean Curvature Equation

In this paper, we study the asymptotic behavior of Palais-Smale sequences associated with the prescribed mean curvature equation on a compact manifold with boundary. We prove that every such sequence converges to a solution of the associated equation plus finitely many “bubbles” obtained by rescaling fundamental solutions of the corresponding Euclidean boundary value problem.

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