De Giorgi Techniques Applied to The Holder Regularity of Solutions to Hamilton-Jacobi Equations

TL;DR

This paper demonstrates that De Giorgi techniques can establish Holder regularity for solutions to Hamilton-Jacobi equations, showing regularization effects that do not depend on the Hamiltonian's regularity.

Contribution

It introduces a novel application of De Giorgi methods to prove regularity of Hamilton-Jacobi solutions independently of Hamiltonian smoothness.

Findings

Proves C^{eta} regularization for Hamilton-Jacobi solutions

Regularization effect is independent of Hamiltonian regularity

Uses De Giorgi method for the first time in this context

Abstract

This article is dedicated to the proof of C^{\alpha} regularization effects of Hamilton- Jacobi equations. The proof is based on the De Giorgi method. The regularization is independent on the regularity of the Hamiltonian.