On estimates for fully nonlinear elliptic equations with Neumann boundary conditions on Riemannian Manifolds

2018/11/29 by Bo Guan, Guan, Bo, Xiang Ni +1
Computer Science · Mathematics · #35B45 #35J15 #35J25 #35J66 #58J05 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1811.12448

openalex publication_date 2018/11/29 · openalex created_date 2018/12/11 · openalex updated_date 2026/07/28

Abstract

We derive gradient and second order \em a priori estimates for solutions of the Neumann problem for a general class of fully nonlinear elliptic equations on compact Riemannian manifolds with boundary. These estimates yield regularity and existence results.

Citations

• Conformal geometry, contact geometry, and the calculus of variations
• Estimates and existence results for a fully nonlinear Yamabe problem on manifolds with boundary

Related

• On Neumann problems for elliptic and parabolic equations on bounded manifolds
• Regularity of fully non-linear elliptic equations on Hermitian manifolds
• Regularity of fully non-linear elliptic equations on Hermitian manifolds. III
• Second order estimates for fully nonlinear elliptic equations with gradient terms on Hermitian manifolds
• Second order estimates for Hessian type fully nonlinear elliptic equations on Riemannian manifolds