Global subanalytic solutions of Hamilton-Jacobi type equations
type: Dataset
description: In the 80's, Crandall and Lions introduced the concept of viscosity solution, in order to get existence and/or uniqueness results for Hamilton-Jacobi equations. In this work, we first investigate the Dirichlet and Cauchy-Dirichlet problems for such equations, where the Hamiltonian is associated to a problem of calculus of variations, and prove that, if the data are analytic, then the viscosity solution is moreover subanalytic. We then extend this result to Hamilton-Jacobi equations stemming from optimal control problems, in particular from sub-Riemannian geometry, which are generalized eikonal equations. As a consequence, the set of singularities of the viscosity solutions of such Hamilton-Jacobi equations is a subanalytic stratified manifold of codimension greater than or equal to one.
issued: 2026-05-09T16:44:54.703580
language: en
modified: 2026-05-09T16:44:54.703584
contact point: Organization
  fn: CCSD
keyword: 49l25-32b20
keyword: hamilton-jacobi-equation
keyword: infoeu-reposemanticsarticle
keyword: journal-articles
keyword: mathmath-ocmathematics-mathoptimization-and-control-mathoc
keyword: subanalytic-sets
keyword: value-function
keyword: viscosity-solution
landing page: 0294-1449

Global subanalytic solutions of Hamilton-Jacobi type equations
type: Distribution
format: HTML
issued: 2026-05-09T16:44:54.708215
modified: 2026-05-09T16:44:54.693442
access URL: https://hal.science/hal-00086360

test_moissonnage_selune
type: Agent