# Representation formulas for contact type Hamilton-Jacobi equations

## TL;DR

This paper explores different representation formulas for viscosity solutions of contact type Hamilton-Jacobi equations using Herglotz' variational principle, enhancing understanding of their structure and solution methods.

## Contribution

It introduces new representation formulas for contact type Hamilton-Jacobi equations based on Herglotz' variational principle, expanding the theoretical framework.

## Key findings

- Derived new representation formulas for viscosity solutions.
- Connected Herglotz' variational principle to contact Hamilton-Jacobi equations.
- Provided insights into the structure of solutions.

## Abstract

We discuss various kinds of representation formulas for the viscosity solutions of the contact type Hamilton-Jacobi equations by using the Herglotz' variational principle.