메뉴 건너뛰기




Volumn 48, Issue 3, 1999, Pages 993-1035

Hopf-Lax Formulas for Semicontinuous Data

Author keywords

Hopf and Lax formulas; Level sets; lsc viscosity solutions

Indexed keywords


EID: 0001262246     PISSN: 00222518     EISSN: None     Source Type: Journal    
DOI: 10.1512/iumj.1999.48.1648     Document Type: Article
Times cited : (53)

References (25)
  • 2
    • 0001324581 scopus 로고
    • On Hopf's formulas for solutions of Hamilton Jacobi equations
    • M. BARDI & L. C. EVANS, On Hopf's formulas for solutions of Hamilton Jacobi equations, Nonlinear Anal., TMA 8 (1984), 1373-1381.
    • (1984) Nonlinear Anal., TMA , vol.8 , pp. 1373-1381
    • Bardi, M.1    Evans, L.C.2
  • 4
    • 0003267441 scopus 로고
    • Solutions de Viscosité des Equations de Hamilton-Jacobi
    • Springer Verlag, New York
    • G. BARLES, Solutions de Viscosité des Equations de Hamilton-Jacobi, Mathematiques & Applications 17, Springer Verlag, New York, 1994.
    • (1994) Mathematiques & Applications , vol.17
    • Barles, G.1
  • 5
    • 78049400271 scopus 로고
    • Semicontinuous viscosity solutions for Hamilton Jacobi equations with convex Hamiltonians
    • E. N. BARRON & R. JENSEN, Semicontinuous viscosity solutions for Hamilton Jacobi equations with convex Hamiltonians, Comm. PDE 15 (1990), 1713-1742.
    • (1990) Comm. PDE , vol.15 , pp. 1713-1742
    • Barron, E.N.1    Jensen, R.2
  • 6
    • 84968515664 scopus 로고
    • Optimal control and semicontinuous viscosity solutions
    • _, Optimal control and semicontinuous viscosity solutions, Proc. Amer. Math. Soc. 113 (1991), 397-402.
    • (1991) Proc. Amer. Math. Soc. , vol.113 , pp. 397-402
  • 8
    • 0030296123 scopus 로고    scopus 로고
    • ∞ control problem
    • ∞ control problem, Appl. Math. & Optimization 34 (1996), 325-360.
    • (1996) Appl. Math. & Optimization , vol.34 , pp. 325-360
  • 10
    • 0013529180 scopus 로고    scopus 로고
    • t + H(u, Du) = 0, II
    • t + H(u, Du) = 0, II, Comm. PDE 22 (1997), 1141-1160.
    • (1997) Comm. PDE , vol.22 , pp. 1141-1160
  • 11
    • 84875084308 scopus 로고    scopus 로고
    • Explicit solution of some first order pde's
    • _, Explicit solution of some first order pde's, J. Dynamical and Control Systems 3 (1997), 1-16.
    • (1997) J. Dynamical and Control Systems , vol.3 , pp. 1-16
  • 12
    • 0032362359 scopus 로고    scopus 로고
    • t + H(u, Du) = 0
    • t + H(u, Du) = 0, SIAM J. Math. Anal. 29 (1998), 1022-1039.
    • (1998) SIAM J. Math. Anal. , vol.29 , pp. 1022-1039
  • 14
    • 84972518016 scopus 로고
    • Motion of level sets by mean curvature. I
    • L. C. EVANS & J. SPRUCK, Motion of level sets by mean curvature. I., J. Differential Geom. 33 (1991), 635-681.
    • (1991) J. Differential Geom. , vol.33 , pp. 635-681
    • Evans, L.C.1    Spruck, J.2
  • 15
    • 84972499852 scopus 로고
    • Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations
    • Y. G. CHEN, Y. GIGA & S. GOTO, Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations, J. Differential Geom. 33 (1991), 749-786.
    • (1991) J. Differential Geom. , vol.33 , pp. 749-786
    • Chen, Y.G.1    Giga, Y.2    Goto, S.3
  • 16
    • 84972546686 scopus 로고
    • Generalized motion of noncompact hypersurfaces with velocity having arbitrary growth on the curvature tensor
    • H. ISHII & P. SOUGANIDIS, Generalized motion of noncompact hypersurfaces with velocity having arbitrary growth on the curvature tensor, Tohoku Math. J. (2) 47 (1995), 227-250.
    • (1995) Tohoku Math. J. , vol.47 , Issue.2 , pp. 227-250
    • Ishii, H.1    Souganidis, P.2
  • 17
    • 0000073921 scopus 로고
    • Generalized solutions of nonlinear equations of first order
    • E. HOPF, Generalized solutions of nonlinear equations of first order, J. Math. Mech. 14 (1965), 951-973.
    • (1965) J. Math. Mech. , vol.14 , pp. 951-973
    • Hopf, E.1
  • 18
    • 84968501412 scopus 로고
    • Hopf formula and multitime Hamilton Jacobi equations
    • P.-L. LIONS & J.-C. ROCHET, Hopf formula and multitime Hamilton Jacobi equations, Proc. Amer. Math. Soc. 96 (1986), 79-84.
    • (1986) Proc. Amer. Math. Soc. , vol.96 , pp. 79-84
    • Lions, P.-L.1    Rochet, J.-C.2
  • 19
    • 0039852357 scopus 로고
    • On lower subdifferentiable functions
    • 'Trends in Mathematical Optimization', ed. by K. H. Hoffman, J. B. Hiriart-Urruty, C. Lemarchal & J. Zowe
    • J. E. MARTINEZ-LEGAZ, On lower subdifferentiable functions, in: 'Trends in Mathematical Optimization', ed. by K. H. Hoffman, J. B. Hiriart-Urruty, C. Lemarchal & J. Zowe, International series Numer. Math., 84 (1988), pp. 197-232.
    • (1988) International Series Numer. Math. , vol.84 , pp. 197-232
    • Martinez-Legaz, J.E.1
  • 20
    • 84963178874 scopus 로고
    • Quasiconvex duality theory by generalized conjugation methods
    • _, Quasiconvex duality theory by generalized conjugation methods, Optimization 19 (1988), 603-652.
    • (1988) Optimization , vol.19 , pp. 603-652
  • 22
    • 0004267646 scopus 로고
    • Princeton University Press, Princeton, New Jersey
    • R. T. ROCKAFELLAR, Convex Analysis, Princeton University Press, Princeton, New Jersey, 1970.
    • (1970) Convex Analysis
    • Rockafellar, R.T.1
  • 23
    • 0003720689 scopus 로고
    • Generalized Concavity in Optimization and Economics
    • Academic Press, New York, J.-P. Crouzeix
    • n, pp. 109-130; A duality framework in quasiconvex programming, pp. 207-226.
    • (1981) n , pp. 109-130
    • Schaible, S.1    Ziemba, W.T.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.