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Regular and Chaotic Dynamics, 2013, Volume 18, Issue 6, Pages 674–685
DOI: https://doi.org/10.1134/S1560354713060075 (Mi rcd155) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Semi-concave Singularities and the Hamilton–Jacobi Equation

Patrick Bernardab

a École normale supérieure – Paris, 75230 Paris Cedex 05, France
b Université Paris-Dauphine – CEREMADE (UMR 7534), Place du Maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France
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DOI: https://doi.org/10.1134/S1560354713060075
Abstract: We study the Cauchy problem for the Hamilton–Jacobi equation with a semiconcave initial condition.We prove an inequality between two types of weak solutions emanating from such an initial condition (the variational and the viscosity solution).We also give conditions for an explicit semi-concave function to be a viscosity solution. These conditions generalize the entropy inequality characterizing piecewise smooth solutions of scalar conservation laws in dimension one.
Keywords: Hamilton–Jacobi equations, viscosity solutions, variational solutions, calculus of variations.
Received: 31.07.2013
Accepted: 08.10.2013
Bibliographic databases:
Document Type: Article
MSC: 49L25, 37J05
Language: English
Citation: Patrick Bernard, “Semi-concave Singularities and the Hamilton–Jacobi Equation”, Regul. Chaotic Dyn., 18:6 (2013), 674–685
Citation in format AMSBIB
\Bibitem{Ber13}
\by Patrick Bernard
\paper Semi-concave Singularities and the Hamilton–Jacobi Equation
\jour Regul. Chaotic Dyn.
\yr 2013
\vol 18
\issue 6
\pages 674--685
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\crossref{https://doi.org/10.1134/S1560354713060075}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3146585}
\zmath{https://zbmath.org/?q=an:1286.49024}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000329108900007}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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