@prefix dcat: <http://www.w3.org/ns/dcat#> .
@prefix dct: <http://purl.org/dc/terms/> .
@prefix foaf: <http://xmlns.com/foaf/0.1/> .
@prefix vcard: <http://www.w3.org/2006/vcard/ns#> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

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    dct: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.
            """ ;
    dct:identifier "hal-00086360" ;
    dct:issued "2026-05-09T16:44:54.703580"^^xsd:dateTime ;
    dct:language "en" ;
    dct:modified "2026-05-09T16:44:54.703584"^^xsd:dateTime ;
    dct:publisher <https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> ;
    dct:title "Global subanalytic solutions of Hamilton-Jacobi type equations" ;
    dcat:contactPoint [ a vcard:Organization ;
            vcard:fn "CCSD" ] ;
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    dcat:keyword "49l25-32b20",
        "hamilton-jacobi-equation",
        "infoeu-reposemanticsarticle",
        "journal-articles",
        "mathmath-ocmathematics-mathoptimization-and-control-mathoc",
        "subanalytic-sets",
        "value-function",
        "viscosity-solution" ;
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    dct:issued "2026-05-09T16:44:54.708215"^^xsd:dateTime ;
    dct:modified "2026-05-09T16:44:54.693442"^^xsd:dateTime ;
    dct:title "Global subanalytic solutions of Hamilton-Jacobi type equations" ;
    dcat:accessURL <https://hal.science/hal-00086360> .

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