A regularity result for viscosity solutions of Hamilton-Jacobi equations in one space dimension

R. Jensen, Panagiotis E. Souganidis

Type: Article

Publication Date: 1987-01-01

Citations: 26

DOI: https://doi.org/10.1090/s0002-9947-1987-0879566-1

Abstract

Viscosity solutions of Hamilton-Jacobi equations need only to be continuous. Here we prove that, in the special case of a one-dimensional stationary problem, under quite general assumptions, Lipschitz continuous viscosity solutions have right and left derivatives at every point. Moreover, these derivatives have some kind of continuity properties.

Locations

University of Minnesota Digital Conservancy (University of Minnesota) - View - PDF
Transactions of the American Mathematical Society - View - PDF

Similar Works

Action	Title	Year	Authors
+	A Regularity Result for Viscosity Solutions of Hamilton-Jacobi Equations in One Space Dimensions	1987	R. Jensen Panagiotis E. Souganidis
+ PDF Chat	On Viscosity Solutions of Certain Hamilton–Jacobi Equations: Regularity Results and Generalized Sard's Theorems	2008	Ludovic Rifford
+ PDF Chat	Regularity of Hamilton-Jacobi equations when forward is backward	1999	E. N. Barron Piermarco Cannarsa R. Jensen Carlo Sinestrari
+	Discontinuous viscosity solutions of first order Hamilton-Jacobi equations	2019	M. Bertsch F. Smarrazzo A. Terracina A. Tesei
+ PDF Chat	A remark about viscosity solutions of Hamilton-Jacobi equations at the boundary	1986	Panagiotis E. Souganidis
+ PDF Chat	On viscosity solutions of certain Hamilton-Jacobi equations: Regularity results and generalized Sard's Theorems	2007	Ludovic Rifford
+	Lipschitz regularity for viscous Hamilton-Jacobi equations with $L^p$ terms	2018	Marco Cirant Alessandro Goffi
+	Lipschitz regularity for viscous Hamilton-Jacobi equations with $L^p$ terms	2018	Marco Cirant Alessandro Goffi
+ PDF Chat	Discontinuous viscosity solutions of first-order Hamilton–Jacobi equations	2021	Michiel Bertsch Flavia Smarrazzo Andrea Terracina Alberto Tesei
+	A Short Introduction to Viscosity Solutions and the Large Time Behavior of Solutions of Hamilton–Jacobi Equations	2013	Hitoshi Ishii
+ PDF Chat	A Remark About Viscosity Solutions of Hamilton-Jacobi Equations at the Boundary	1986	Panagiotis E. Souganidis
+ PDF Chat	Viscosity solutions of discontinuous Hamilton–Jacobi equations	2008	Xinfu Chen Bei Hu
+	Viscosity Solutions of Hamilton-Jacobi Equations	1982	Michael G. Crandall
+	A Dynamical Approach to Viscosity Solutions of Hamilton-Jacobi Equations	2013	Lin Wang Jun Yan
+	Viscosity Solutions	2017	Giorgio Fabbri Fausto Gozzi Andrzej Święch
+	Some Properties of Viscosity Solutions of Hamilton-Jacobi Equations.	1982	M. G. Crandall L. C. Evans Pierre‐Louis Lions
+ PDF Chat	Geometric Conditions for Regularity of Viscosity Solution to the Simplest Hamilton-Jacobi Equation	2013	Vladimir V. Goncharov Fátima Pereira
+	Discontinuous viscosity solutions of first-order Hamilton-Jacobi equations: a guided visit	1993	Guy Barles
+	Hamilton-Jacobi equations with their Hamiltonians depending Lipschitz continuously on the unknown	2021	Hitoshi Ishii Kaizhi Wang Lin Wang Jun Yan
+ PDF Chat	Lipschitz regularity for viscous Hamilton-Jacobi equations with Lp terms	2020	Marco Cirant Alessandro Goffi

Works That Cite This (21)

Action	Title	Year	Authors
+	Convergence and Rates for Hamilton-Jacobi Equations with Kirchoff Junction Conditions	2018	Peter S. Morfe
+	Travelling graphs for the forced mean curvature motion in an arbitrary space dimension Ondes progressives pour le mouvement par courbure moyenne force en toute dimension d'espace	2011	Jean‐Michel Roquejoffre Violaine Roussier-Michon
+	A comparison among various notions of viscosity solution for Hamilton–Jacobi equations on networks	2013	Fabio Camilli Claudio Marchi
+ PDF Chat	Regularity Through Approximation for Scalar Conservation Laws	1988	Bradley J. Lucier
+ PDF Chat	Convergence & rates for Hamilton–Jacobi equations with Kirchoff junction conditions	2020	Peter S. Morfe
+	Formation of singularities for viscosity solutions of hamilton—jacobi equations in one space variable	1993	Georgios T. Kossioris
+ PDF Chat	Viscosity solutions for junctions: well posedness and stability	2016	Pierre-Louis Lions Panagiotis E. Souganidis
+ PDF Chat	Well-posedness for multi-dimensional junction problems with Kirchoff-type conditions	2017	Pierre-Louis Lions Panagiotis E. Souganidis
+	User’s guide to viscosity solutions of second order partial differential equations	1992	Michael G. Crandall Hitoshi Ishii Pierre-Louis Lions
+	user's guide to viscosity solutions of second order partial differential equations	1992	Michael G. Crandall Hitoshi Ishii Pierre‐Louis Lions

Works Cited by This (9)

Action	Title	Year	Authors
+	Developments in the Theory of Nonlinear First-Order Partial Differential Equations	1984	Michael G. Crandall Panagiotis E. Souganidis
+	The Cauchy problem for a nonlinear first order partial differential equation	1969	Wendell H. Fleming
+ PDF Chat	Some properties of viscosity solutions of Hamilton-Jacobi equations	1984	Michael G. Crandall L. C. Evans Pierre‐Louis Lions
+	Regularity and large time behaviour of solutions of a conservation law without convexity	1985	Constantine M. Dafermos
+ PDF Chat	Partial Differential Equations	1988	Shiing-Shen Chern
+ PDF Chat	Viscosity Solutions of Hamilton-Jacobi Equations	1983	Michael G. Crandall Pierre‐Louis Lions
+	Uniqueness and stability of the generalized solution of the Cauchy problem for a quasi-linear equation	1963	O. A. Oleĭnik
+ PDF Chat	Some Properties of Viscosity Solutions of Hamilton-Jacobi Equations	1984	Michael G. Crandall L. C. Evans Pierre Louis Lions
+	On the Singularities of the Viscosity Solutions to Hamilton-Jacobi-Bellman Equations	1985	Piermarco Cannarsa H. Meté Soner