Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Commutation Properties of Semi-groups for Contact Type Hamilton-Jacobi Equation

Guyu Jin

Abstract

We know that there exist semi-groups for contact type Hamilton-Jacobi equations, which refers to \cite{KLJ2}. Guy Barles and Agnès Tourin give a proof of the commutation properties for normal Hamilton-Jacobi equations at \cite{GA}. In this article, we provide a proof of the commutation property of semi-groups for contact type Hamilton-Jacobi equations.

Commutation Properties of Semi-groups for Contact Type Hamilton-Jacobi Equation

Abstract

We know that there exist semi-groups for contact type Hamilton-Jacobi equations, which refers to \cite{KLJ2}. Guy Barles and Agnès Tourin give a proof of the commutation properties for normal Hamilton-Jacobi equations at \cite{GA}. In this article, we provide a proof of the commutation property of semi-groups for contact type Hamilton-Jacobi equations.
Paper Structure (4 sections, 17 theorems, 93 equations)

This paper contains 4 sections, 17 theorems, 93 equations.

Table of Contents

  1. Introduction
  2. Proof of Theorem 3
  3. Further results and extensions
  4. Proof of Theorem 8

Key Result

Proposition 1.1

Assume that $H$ satisfies (H1)-(H4), then there exists the unique Lipschitz viscosity solution of (HJ).

Theorems & Definitions (33)

  • Definition 1.1
  • Proposition 1.1
  • proof
  • Definition 1.2
  • Proposition 1.2: Implicit Variational Principle
  • Theorem 1
  • Definition 1.3
  • Lemma 1.1
  • Proposition 1.3
  • Lemma 1.2
  • ...and 23 more