The double obstacle problem on non divergence form

TL;DR

This paper investigates the regularity of solutions to the double obstacle problem for fully nonlinear parabolic and elliptic operators, establishing interior $C^{1,eta}$ regularity when obstacles are sufficiently smooth.

Contribution

It proves interior regularity results for solutions to the double obstacle problem in the fully nonlinear setting, extending known results to non divergence form operators.

Findings

Solutions are $C^{1,eta}$ in the interior when obstacles are regular.

Regularity results apply to both parabolic and elliptic cases.

The work extends regularity theory to fully nonlinear non divergence form operators.

Abstract

We study the regularity of the solution of the double obstacle problem form for fully non linear parabolic and elliptic operators. We show that when the obstacles are sufficiently regular the solution is $C^{1,\alpha}$ in the interior for both the parabolic and the elliptic cases.