메뉴 건너뛰기




Volumn 5, Issue 4, 2006, Pages 793-812

Minimax and viscosity solutions of Hamilton-jacobi equations in the convex case

Author keywords

Hamilton Jacobi theory; Symplectic topology; Viscosity solutions

Indexed keywords


EID: 33751172330     PISSN: 15340392     EISSN: 15535258     Source Type: Journal    
DOI: 10.3934/cpaa.2006.5.793     Document Type: Article
Times cited : (8)

References (34)
  • 1
    • 0001170185 scopus 로고
    • Symplectic geometry
    • Basel
    • B. Aebischer et al, Symplectic geometry, Progress in Mathematics, Basel, Vol XII, 124 pp. (1994).
    • (1994) Progress in Mathematics , vol.12
    • Aebischer, B.1
  • 3
    • 0038862733 scopus 로고    scopus 로고
    • Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations
    • Boston, MA: Birkhauser
    • M. Bardi and I. Capuzzo-Dolcetta, Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations, Systems and Control: Foundations and Applications. Boston, MA: Birkhauser. xvii, 570 pp. (1997).
    • (1997) Systems and Control: Foundations and Applications , vol.17
    • Bardi, M.1    Capuzzo-Dolcetta, I.2
  • 4
    • 84889146512 scopus 로고
    • Symplectic relations in analytical mechanics
    • Modern developments in analytical mechanics, Vol. I: Geometrical dynamics, Torino, Italy 1982
    • S. Benenti, Symplectic relations in analytical mechanics. Modern developments in analytical mechanics, Vol. I: Geometrical dynamics, Proc. IUTAM-ISIMM Symp., Torino, Italy 1982, 39-91, (1983).
    • (1983) Proc. IUTAM-ISIMM Symp. , pp. 39-91
    • Benenti, S.1
  • 6
    • 33751167609 scopus 로고    scopus 로고
    • Landscapes of necessary conditions for the maxima in optimal control using Lagrangian submanifolds' global parameterizations and generalized solutions
    • Geom. Zadachi Teor. Upr.
    • P. Bettiol and F. Cardin, Landscapes of necessary conditions for the maxima in optimal control using Lagrangian submanifolds' global parameterizations and generalized solutions. (Russian) Sovrem. Mat. Prilozh. No. 21, Geom. Zadachi Teor. Upr., 36-55, (2004).
    • (2004) (Russian) Sovrem. Mat. Prilozh. No. 21 , pp. 36-55
    • Bettiol, P.1    Cardin, F.2
  • 7
    • 33751178576 scopus 로고    scopus 로고
    • The Hopf solution of Hamilton-Jacobi equations
    • Bemelmans, Josef (ed.) et al., Rolduc, Netherlands, June 18-22, 2001 and Gaeta, Italy, September 24-28, 2001. Singapore: World Scientific.
    • I. Capuzzo Dolcetta, The Hopf solution of Hamilton-Jacobi equations, Bemelmans, Josef (ed.) et al., Elliptic and parabolic problems. Proceedings of the 4th European conference, Rolduc, Netherlands, June 18-22, 2001 and Gaeta, Italy, September 24-28, 2001. Singapore: World Scientific., 343-351, (2002).
    • (2002) Elliptic and Parabolic Problems. Proceedings of the 4th European Conference , pp. 343-351
    • Capuzzo Dolcetta, I.1
  • 8
    • 38249001625 scopus 로고
    • On viscosity and geometrical solutions of Hamilton-Jacobi equations
    • F. Cardin, On viscosity and geometrical solutions of Hamilton-Jacobi equations, Nonlinear Anal., Theory Methods Appl., (6) 20 (1993), 713-719.
    • (1993) Nonlinear Anal., Theory Methods Appl., (6) , vol.20 , pp. 713-719
    • Cardin, F.1
  • 9
    • 0035981960 scopus 로고    scopus 로고
    • The global finite structure of generic envelope loci for Hamilton-Jacobi equations
    • F. Cardin, The global finite structure of generic envelope loci for Hamilton-Jacobi equations, J. Math. Phys., (1) 43 (2002), 417-430.
    • (2002) J. Math. Phys., (1) , vol.43 , pp. 417-430
    • Cardin, F.1
  • 12
    • 0001355549 scopus 로고
    • Quelques questions de géométrie symplectique
    • M. Chaperon, Quelques questions de géométrie symplectique, Séminarie Bourbaki, 610 (1983), 231-249.
    • (1983) Séminarie Bourbaki , vol.610 , pp. 231-249
    • Chaperon, M.1
  • 13
    • 0039852291 scopus 로고
    • Lois de conservation et géométrie symplectique
    • Séries 1
    • M. Chaperon, Lois de conservation et géométrie symplectique, C. R. Acad. Sci. Paris 312 Séries 1, 345-348, (1991).
    • (1991) C. R. Acad. Sci. Paris , vol.312 , pp. 345-348
    • Chaperon, M.1
  • 14
    • 0002741292 scopus 로고
    • The Birkhoff-Lewis fixed point theorem and a conjecture of V.I. Arnol'd
    • C. Conley and E. Zehnder, The Birkhoff-Lewis fixed point theorem and a conjecture of V.I. Arnol'd, Invent. Math., 73 (1983), 33-49.
    • (1983) Invent. Math. , vol.73 , pp. 33-49
    • Conley, C.1    Zehnder, E.2
  • 16
    • 0002812374 scopus 로고
    • Quantization of the Bellman equation, exponential asymptotics and tunneling
    • Amer. Math. Soc., Providence, RI, Idempotent analysis
    • S.Yu. Dobrokhotov, V.N. Kolokoltsov and V.P. Maslov, Quantization of the Bellman equation, exponential asymptotics and tunneling, Adv. Soviet Math., 13, Amer. Math. Soc., Providence, RI, Idempotent analysis, 1-46, (1992).
    • (1992) Adv. Soviet Math. , vol.13 , pp. 1-46
    • Dobrokhotov, S.Yu.1    Kolokoltsov, V.N.2    Maslov, V.P.3
  • 17
    • 0031138612 scopus 로고    scopus 로고
    • Thèoréme KAM faible et thèorie de Mather sur les systémes lagrangiens
    • Sèrie 1
    • A. Fathi, Thèoréme KAM faible et thèorie de Mather sur les systémes lagrangiens, C. R. Acad. Sci. Paris, 324, Sèrie 1 (1997), 1043-1046.
    • (1997) C. R. Acad. Sci. Paris , vol.324 , pp. 1043-1046
    • Fathi, A.1
  • 23
    • 0003292086 scopus 로고
    • Generalized solutions of Hamilton-Jacobi equations
    • Boston - London - Melbourne: Pitman Advanced Publishing Program
    • P.L. Lions, Generalized solutions of Hamilton-Jacobi equations, Research Notes in Mathematics, 69. Boston - London - Melbourne: Pitman Advanced Publishing Program. 317 pp. (1982).
    • (1982) Research Notes in Mathematics , vol.69
    • Lions, P.L.1
  • 27
    • 0036391686 scopus 로고    scopus 로고
    • The relationship between two approaches to a generalized solution of the Hamilton-Jacobi equation
    • I.V.Rublev, The relationship between two approaches to a generalized solution of the Hamilton-Jacobi equation, Differ. Equ., (6) 38 (2002), 865-873.
    • (2002) Differ. Equ., (6) , vol.38 , pp. 865-873
    • Rublev, I.V.1
  • 28
    • 14844324328 scopus 로고
    • Sur les immersions lagrangiennes dans un fibré cotangent admettant une phase génératrice globale
    • 302, Sér. I
    • J.C.Sikorav, Sur les immersions lagrangiennes dans un fibré cotangent admettant une phase génératrice globale. C. R. Acad. Sci., Paris, 302, Sér. I, 3 (1986), 119-122.
    • (1986) C. R. Acad. Sci., Paris , vol.3 , pp. 119-122
    • Sikorav, J.C.1
  • 30
    • 33751162114 scopus 로고    scopus 로고
    • Minimax solutions to the Hamilton-Jacobi equations
    • New York
    • A.I.Subbotin, Minimax solutions to the Hamilton-Jacobi equations, J. Math. Sci., New York 103, No.6, 772-777, (2001).
    • (2001) J. Math. Sci. , vol.103 , Issue.6 , pp. 772-777
    • Subbotin, A.I.1
  • 31
    • 0348031469 scopus 로고    scopus 로고
    • A complete proof of Viterbo's uniqueness theorem on generating functions
    • D. Theret, A complete proof of Viterbo's uniqueness theorem on generating functions, Topology and its applications, 96 (1999), 249-266.
    • (1999) Topology and Its Applications , vol.96 , pp. 249-266
    • Theret, D.1
  • 34
    • 0003360567 scopus 로고
    • Lectures on symplectic manifolds
    • Conference Board of the Mathematical Sciences. Providence, R. I.: AMS
    • A. Weinstein, Lectures on symplectic manifolds, Conference Board of the Mathematical Sciences, Regional Conference Series in Mathematics. Number 29. Providence, R. I.: AMS, (1977).
    • (1977) Regional Conference Series in Mathematics , Issue.29
    • Weinstein, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.