Fully nonlinear second order elliptic equations with large zeroth order coefficient

Perturbing Fully Nonlinear Second Order Elliptic Equations

We present two types of perturbations with reverse effects on some scalar fully nonlinear second order elliptic differential operators: on the other hand, first order perturbations which destroy the global solvability of the Dirichlet problem, in smooth bounded domains of Rn; on the other hand, an integral perturbation which restore the local solvability, on compact connected manifolds without ...

Existence and Comparison Results for Fully Nonlinear Degenerate Elliptic Equations without Zeroth-Order Term

Local Discontinuous Galerkin Methods for One-Dimensional Second Order Fully Nonlinear Elliptic and Parabolic Equations

This paper is concerned with developing accurate and efficient nonstandard discontinuous Galerkin methods for fully nonlinear second order elliptic and parabolic partial differential equations (PDEs) in the case of one spatial dimension. The primary goal of the paper to develop a general framework for constructing high order local discontinuous Galerkin (LDG) methods for approximating viscosity...

The Second Order Estimate for Fully Nonlinear Uniformly Elliptic Equations without Concavity Assumption

Investigating for interior regularity of viscosity solutions to the fully nonlinear elliptic equation F (x, u,▽u,▽u) = 0, we establish the interior C continuity under the assumptions that F is uniformly elliptic, Hölder continuous and satisfies the natural structure conditions of fractional order, but without the concavity assumption of F . These assumptions are weaker and the result is stronge...

Second Order Estimates and Regularity for Fully Nonlinear Elliptic Equations on Riemannian Manifolds

We derive a priori second order estimates for solutions of a class of fully nonlinear elliptic equations on Riemannian manifolds under structure conditions which are close to optimal. We treat both equations on closed manifolds, and the Dirichlet problem on manifolds with boundary without any geometric restrictions to the boundary. These estimates yield regularity and existence results some of ...