On the Dirichlet Problem for Non-totally Degenerate Fully Nonlinear Elliptic Equations

Interior Regularity of Fully Nonlinear Degenerate Elliptic Equations I: Bellman Equations with Constant Coefficients

This is the first of a series of papers on the interior regularity of fully nonlinear degenerate elliptic equations of second order. We consider here a stochastic optimal control problem in a domain, in which the diffusion coefficients, drift coefficients and discount factor are independent of the spatial variables. Under appropriate assumptions, for k = 0, 1, when the terminal and running payo...

Existence Results for a Dirichlet Quasilinear Elliptic Problem

In this paper, existence results of positive classical solutions for a class of second-order differential equations with the nonlinearity dependent on the derivative are established. The approach is based on variational methods.

A Dirichlet Type Problem for Nonlinear Degenerate Elliptic Equations Arising in Time-optimal Stochastic Control

We study general 2nd order fully nonlinear degenerate elliptic equations on an arbitrary closed set with generalized Dirichlet boundary conditions in the viscosity sense. We prove some properties of the maximal subsolution and the minimal supersolution of the Dirichlet type problem. Under a sort of compatibility condition on the boundary data we show that the maximal subsolution is the natural ...

The Dirichlet Problem for Fully Nonlinear Elliptic Equations on Riemannian Manifolds

We study a class of fully nonlinear elliptic equations on Riemannian manifolds and solve the Dirichlet problem in a domain with no geometric restrictions to the boundary under essentially optimal structure conditions. It includes a new (and optimal) result in the Euclidean case (see Theorem 1.1). We introduce some new methods in deriving a priori C estimates, which can be used to treat other ty...

Solvability of Nonlinear Dirichlet Problem for a Class of Degenerate Elliptic Equations