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Volumn 81, Issue 6, 2003, Pages 678-688

On viscosity solutions of irregular Hamilton-Jacobi equations

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EID: 0346307635     PISSN: 0003889X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00013-003-0573-y     Document Type: Article
Times cited : (12)

References (12)
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  • 2
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    • I. CAPUZZO DOLCETTA and B. PERTHAME, On some analogy between different approaches to first order PDE's with nonsmooth coefficients. Adv. Math. Sci. Appl. 6, 689-703 (1996).
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  • 3
    • 0036487117 scopus 로고    scopus 로고
    • Uniqueness of continuous solutions for BV vector fields
    • F. COLOMBINI and N. LERNER, Uniqueness of continuous solutions for BV vector fields. Duke Math. J. 111, 357-384 (2002).
    • (2002) Duke Math. J. , vol.111 , pp. 357-384
    • Colombini, F.1    Lerner, N.2
  • 4
    • 0000446066 scopus 로고
    • Generalized solutions of linear differential equations with discontinuous coefficients and the uniqueness question for multidimensional quasilinear conservation laws
    • E. CONWAY, Generalized solutions of linear differential equations with discontinuous coefficients and the uniqueness question for multidimensional quasilinear conservation laws. J. Math. Anal. Appl. 18, 238-251 (1967).
    • (1967) J. Math. Anal. Appl. , vol.18 , pp. 238-251
    • Conway, E.1
  • 5
    • 84972545750 scopus 로고
    • Uniqueness of viscosity solutions of Hamilton-Jacobi equations revisited
    • M.G. CRANDALL, H. ISHII and P.-L. LIONS, Uniqueness of viscosity solutions of Hamilton-Jacobi equations revisited. J. Math. Soc. Japan 39, 581-596 (1987).
    • (1987) J. Math. Soc. Japan , vol.39 , pp. 581-596
    • Crandall, M.G.1    Ishii, H.2    Lions, P.-L.3
  • 6
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    • User's guide to viscosity solutions of second order partial differential equations
    • 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. (N.S.) 27, 1-67 (1992).
    • (1992) Bull. Amer. Math. Soc. (N.S.) , vol.27 , pp. 1-67
    • Crandall, M.G.1    Ishii, H.2    Lions, P.-L.3
  • 7
    • 84972578354 scopus 로고
    • Remarks on the existence and uniqueness of unbounded viscosity solutions of Hamilton-Jacobi equations
    • M.G. CRANDALL and P.-L. LIONS, Remarks on the existence and uniqueness of unbounded viscosity solutions of Hamilton-Jacobi equations. Illinois J. Math. 31, 665-688 (1987).
    • (1987) Illinois J. Math. , vol.31 , pp. 665-688
    • Crandall, M.G.1    Lions, P.-L.2
  • 8
    • 0002306354 scopus 로고
    • Ordinary differential equations, transport theory and Sobolev spaces
    • R.J. DIPERNA and P.-L. LIONS, Ordinary differential equations, transport theory and Sobolev spaces. Invent. Math. 98, 511-547 (1989).
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    • Diperna, R.J.1    Lions, P.-L.2
  • 9
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    • Linear transport equations with discontinuous coefficients
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    • Petrova, G.1    Popov, B.2
  • 10
    • 0035882842 scopus 로고    scopus 로고
    • Linear transport equations with μ-monotone coefficients
    • G. PETROVA and B. POPOV, Linear transport equations with μ-monotone coefficients. J. Math. Anal. Appl. 260, 307-324 (2001).
    • (2001) J. Math. Anal. Appl. , vol.260 , pp. 307-324
    • Petrova, G.1    Popov, B.2
  • 12
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    • Local error estimates for discontinuous solutions of nonlinear hyperbolic equations
    • E. TADMOR, Local error estimates for discontinuous solutions of nonlinear hyperbolic equations. SIAM J. Numer. Anal. 28, 891-906 (1991).
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    • Tadmor, E.1


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