Interior regularity of fully nonlinear degenerate elliptic equations, I: Bellman equations with constant coefficients

Abstract

This is the first of a series of papers on the interior regularity of fully nonlinear degenerate elliptic equations. We consider a stochastic optimal control problem in which the diffusion coefficients, drift coefficients and discount factor are independent of the spacial variables. Under suitable assumptions, for $k=0,1$, when the terminal and running payoffs are globally $C^{k,1}$, we obtain the $C^{k,1}$-smoothness of the value function, which yields the existence and uniqueness of the solution to the associated Dirichlet problem for the degenerate Bellman equation.

arXiv commentAssumption 2.2 was corrected and then weakened. The original Assumption 2.2 after correction is now Remark 2.1. Minor revision was made accordingly on pages 28 and 29. A few typos were corrected also

References in corpus (1)

• Interior regularity of fully nonlinear degenerate elliptic equations, II: real and complex Monge-Ampère equations

Cited by in corpus (3)

• Representation and regularity for the Dirichlet problem for real and complex degenerate Hessian equations
• Interior regularity of fully nonlinear degenerate elliptic equations, II: real and complex Monge-Ampère equations
• On representation and regularity of viscosity solutions to degenerate Isaacs equations and certain nonconvex Hessian equations