Herglotz' generalized variational principle and contact type Hamilton-Jacobi equations

TL;DR

This paper introduces a new approach to analyze solutions of contact type Hamilton-Jacobi equations using Herglotz's generalized variational principle, along with Lipschitz estimates for minimizers.

Contribution

It extends the variational framework to contact Hamilton-Jacobi equations, providing new analytical tools and quantitative estimates.

Findings

Established a variational approach for contact Hamilton-Jacobi equations

Derived Lipschitz estimates for minimizers

Enhanced understanding of fundamental solutions in this context

Abstract

We develop an approach for the analysis of fundamental solutions to Hamilton-Jacobi equations of contact type based on a generalized variational principle proposed by Gustav Herglotz. We also give a quantitative Lipschitz estimate on the associated minimizers.