Local Lipschitz regularity for functions satisfying a time-dependent dynamic programming principle

TL;DR

This paper demonstrates that functions adhering to a time-dependent dynamic programming principle exhibit local Lipschitz regularity, linking to the normalized parabolic p-Laplace operator, and advancing understanding of regularity in such functions.

Contribution

It establishes local Lipschitz regularity for functions satisfying a specific time-dependent dynamic programming principle, connecting it to the normalized parabolic p-Laplace operator.

Findings

Functions satisfying the DPP are locally Lipschitz continuous.

The result connects DPP solutions to parabolic p-Laplace regularity.

Provides a foundation for further regularity analysis in related PDEs.

Abstract

We prove in this article that functions satisfying a dynamic programming principle have a local interior Lipschitz type regularity. This DPP is partly motivated by the connection to the normalized parabolic $p$-Laplace operator.