# On Lp-viscosity solutions of bilateral obstacle problems with unbounded ingredients

## TL;DR

This paper establishes continuity and existence results for Lp-viscosity solutions of bilateral obstacle problems with unbounded ingredients, extending regularity estimates under minimal obstacle regularity.

## Contribution

It provides the first global equi-continuity estimate for solutions with merely continuous obstacles and proves existence via data approximation, also deriving local Hölder estimates for smoother obstacles.

## Key findings

- Global equi-continuity estimate for solutions with continuous obstacles
- Existence of solutions via approximation of data
- Local Hölder continuity of derivatives for smooth obstacles

## Abstract

The global equi-continuity estimate on Lp-viscosity solutions of bilateral obstacle problems with unbounded ingredients is established when obstacles are merely continuous. The existence of Lp-viscosity solutions is established via an approximation of given data. The local H\"older continuity estimate on the first derivative of Lp-viscosity solutions is shown when the obstacles belong to C^{1,\beta}, and p>n.