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Almost classical solutions of Hamilton-Jacobi equations

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dc.contributor.authorDeville, Robert
dc.contributor.authorJaramillo Aguado, Jesús Ángel
dc.date.accessioned2023-06-20T09:39:17Z
dc.date.available2023-06-20T09:39:17Z
dc.date.issued2008
dc.description.abstractWe study the existence of everywhere differentiable functions which are almost everywhere solutions of quite general Hamilton-Jacobi equations on open subsets of R(d) or on d-dimensional manifolds whenever d >= 2. In particular, when M is a Riemannian manifold, we prove the existence of a differentiable function a on M which satisfies the Eikonal equation parallel to del u(x)parallel to(x) = 1 almost everywhere on M.
dc.description.departmentDepto. de Análisis Matemático y Matemática Aplicada
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.sponsorshipMinisterio de Ciencia e Innovación (MICINN)
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/16596
dc.identifier.doi10.4171/RMI/564
dc.identifier.issn0213-2230
dc.identifier.officialurlhttp://projecteuclid.org/euclid.rmi/1228834302
dc.identifier.relatedurlhttp://projecteuclid.org
dc.identifier.urihttps://hdl.handle.net/20.500.14352/50121
dc.issue.number3
dc.journal.titleRevista Matemática Iberoamericana
dc.language.isoeng
dc.page.final1010
dc.page.initial989
dc.publisherUniv Autónoma Madrid
dc.relation.projectIDMTM2006-03531
dc.rights.accessRightsopen access
dc.subject.cdu517.55
dc.subject.keywordRiemannian-Manifolds
dc.subject.keywordGradient Problem
dc.subject.keywordHamilton-Jacobi Equations
dc.subject.keywordEikonal Equation On Manifolds
dc.subject.keywordAlmost Everywhere Solutions
dc.subject.ucmMatemáticas (Matemáticas)
dc.subject.ucmAnálisis matemático
dc.subject.ucmEcuaciones diferenciales
dc.subject.unesco12 Matemáticas
dc.subject.unesco1202 Análisis y Análisis Funcional
dc.subject.unesco1202.07 Ecuaciones en Diferencias
dc.titleAlmost classical solutions of Hamilton-Jacobi equations
dc.typejournal article
dc.volume.number24
dcterms.referencesD. Azagra, J. Ferrera and F. López-Mesas, Nonsmooth analysis and Hamilton-Jacobi equations on Riemannian manifolds. J. Funct. Anal. 220 (2005) 304–361. G. Barles, Solutions de viscosité des équations de Hamilton-Jacobi. Mathématiques el Applications, 17, Springer-Verlag (1994). M. T. Benameur, Triangulations and the stability theorem for foliations. Pacific J. of Math. 179 (1997) 221–239. Z. Buczolich, Solution to the gradient problem of C. E. Weil. Revista. Mat. Iberoamericana 21 (2005) 889–910. M. G. Crandall, H. Ishii and P. L. Lions, User’s guide to viscosity solutions of second order partial differential equations. Bull. Amer. Math. Soc. 27 (1992) 1–67. R. Deville and É. Matheron, Infinite games, Banach space geometry and the eikonal equation. To appear in Proc. London Math. Soc. J. Malý, M. Zelený, A note on Buczolich’s solution of the Weil gradient problem. Preprint. C. Mantegazza and A. C. Mennucci, Hamilton-Jacobi Equations and Distance Functions on Riemannian Manifods. Appl. Math. and Optim. 47 (2003) 1–25. C. E. Weil, On properties of derivatives. Trans. Amer. Math. Soc. 114 (1965) 363–376. H. Whitney, Geometric integration theory. Princeton Univ. Press, 19 (1957).
dspace.entity.typePublication
relation.isAuthorOfPublication8b6e753b-df15-44ff-8042-74de90b4e3e9
relation.isAuthorOfPublication.latestForDiscovery8b6e753b-df15-44ff-8042-74de90b4e3e9

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