A dynamic programming principle with continuous solutions related to the $p$-Laplacian, $1 < p < \infty$

TL;DR

This paper investigates a dynamic programming principle connected to the p-Laplacian operator, establishing the existence, uniqueness, and continuity of solutions for the case where 1 < p < infinity.

Contribution

It introduces a novel dynamic programming framework for the p-Laplacian, providing rigorous proofs of solution existence, uniqueness, and continuity.

Findings

Proved existence of solutions to the DPP related to the p-Laplacian.

Established uniqueness of solutions under the given framework.

Demonstrated continuity of solutions with respect to problem data.

Abstract

We study a Dynamic Programming Principle related to the $p$-Laplacian for $1 < p < \infty$. The main results are existence, uniqueness and continuity of solutions.