메뉴 건너뛰기




Volumn 192, Issue 2, 2009, Pages 275-310

A comparison principle for Hamilton-Jacobi equations related to controlled gradient flows in infinite dimensions

Author keywords

[No Author keywords available]

Indexed keywords


EID: 62949185876     PISSN: 00039527     EISSN: 14320673     Source Type: Journal    
DOI: 10.1007/s00205-008-0133-5     Document Type: Article
Times cited : (47)

References (39)
  • 2
    • 0001530170 scopus 로고
    • Discontinuous solutions of deterministic optimal stopping time problems
    • G. Barles B. Perthame 1987 Discontinuous solutions of deterministic optimal stopping time problems Math. Methods Num. Anal. 21 557 579
    • (1987) Math. Methods Num. Anal. , vol.21 , pp. 557-579
    • Barles, G.1    Perthame, B.2
  • 3
    • 0024070155 scopus 로고
    • Exit time problems in optimal control and vanishing viscosity method
    • G. Barles B. Perthame 1988 Exit time problems in optimal control and vanishing viscosity method SIAM J. Control Optim. 26 1133 1148
    • (1988) SIAM J. Control Optim. , vol.26 , pp. 1133-1148
    • Barles, G.1    Perthame, B.2
  • 4
    • 0030291175 scopus 로고    scopus 로고
    • Infinite dimensional Hamilton-Jacobi equations and Dirichlet boundary control problems in parabolic type
    • P. Cannarsa M.E. Tessitore 1996 Infinite dimensional Hamilton-Jacobi equations and Dirichlet boundary control problems in parabolic type SIAM J. Control Optim. 34 1831 1847
    • (1996) SIAM J. Control Optim. , vol.34 , pp. 1831-1847
    • Cannarsa, P.1    Tessitore, M.E.2
  • 6
    • 84967758647 scopus 로고
    • Viscosity solutions of Hamilton-Jacobi equations
    • M.G. Crandall P.-L. Lions 1983 Viscosity solutions of Hamilton-Jacobi equations Trans. A. M. S. 277 1 42
    • (1983) Trans. A. M. S. , vol.277 , pp. 1-42
    • Crandall, M.G.1    Lions, P.-L.2
  • 7
    • 46549092471 scopus 로고
    • Hamilton-Jacobi equations in infinite dimensions, PART i
    • M.G. Crandall P.-L. Lions 1985 Hamilton-Jacobi equations in infinite dimensions, PART I J. Funct. Anal. 62 3 379 396
    • (1985) J. Funct. Anal. , vol.62 , Issue.3 , pp. 379-396
    • Crandall, M.G.1    Lions, P.-L.2
  • 8
    • 46149138623 scopus 로고
    • Hamilton-Jacobi equations in infinite dimensions, PART II
    • M.G. Crandall P.-L. Lions 1986 Hamilton-Jacobi equations in infinite dimensions, PART II J. Funct. Anal. 65 3 368 405
    • (1986) J. Funct. Anal. , vol.65 , Issue.3 , pp. 368-405
    • Crandall, M.G.1    Lions, P.-L.2
  • 9
    • 46149127983 scopus 로고
    • Hamilton-Jacobi equations in infinite dimensions, PART III
    • M.G. Crandall P.-L. Lions 1986 Hamilton-Jacobi equations in infinite dimensions, PART III J. Funct. Anal. 68 2 214 247
    • (1986) J. Funct. Anal. , vol.68 , Issue.2 , pp. 214-247
    • Crandall, M.G.1    Lions, P.-L.2
  • 10
    • 44949288472 scopus 로고
    • Hamilton-Jacobi equations in infinite dimensions, PART IV
    • M.G. Crandall P.-L. Lions 1990 Hamilton-Jacobi equations in infinite dimensions, PART IV J. Funct. Anal. 90 2 237 283
    • (1990) J. Funct. Anal. , vol.90 , Issue.2 , pp. 237-283
    • Crandall, M.G.1    Lions, P.-L.2
  • 11
    • 0001295449 scopus 로고
    • Hamilton-Jacobi equations in infinite dimensions, PART v
    • M.G. Crandall P.-L. Lions 1991 Hamilton-Jacobi equations in infinite dimensions, PART V J. Funct. Anal. 97 2 417 465
    • (1991) J. Funct. Anal. , vol.97 , Issue.2 , pp. 417-465
    • Crandall, M.G.1    Lions, P.-L.2
  • 12
    • 0001885872 scopus 로고
    • Hamilton-Jacobi equations in infinite dimensions, PART VII
    • M.G. Crandall P.-L. Lions 1994 Hamilton-Jacobi equations in infinite dimensions, PART VII J. Funct. Anal. 125 1 111 148
    • (1994) J. Funct. Anal. , vol.125 , Issue.1 , pp. 111-148
    • Crandall, M.G.1    Lions, P.-L.2
  • 13
    • 0002308268 scopus 로고
    • Hamilton-Jacobi equations in infinite dimensions, Part VI: Nonlinear A and Tataru's method refined
    • Lecture Notes in Pure and Appl. Math. Dekker, New York
    • Crandall, M.G., Lions, P.-L.: Hamilton-Jacobi equations in infinite dimensions, PART VI: Nonlinear A and Tataru's method refined. Evolution equations, control theory, and biomathematics (Han sur Lesse, 1991), pp. 51-89, Lecture Notes in Pure and Appl. Math., vol. 155. Dekker, New York, 1994
    • (1994) Evolution Equations, Control Theory, and Biomathematics (Han sur Lesse, 1991) , vol.155 , pp. 51-89
    • Crandall, M.G.1    Lions, P.-L.2
  • 14
    • 84967708673 scopus 로고
    • User's guide to viscosity solutions of second order partial differential equations
    • M.G. Crandall H. Ishii P.-L. Lions 1992 User's guide to viscosity solutions of second order partial differential equations Bull. A.M.S., N.S. 27 1 67
    • (1992) Bull. A.M.S., N.S. , vol.27 , pp. 1-67
    • Crandall, M.G.1    Ishii, H.2    Lions, P.-L.3
  • 15
    • 0001356070 scopus 로고
    • Large deviation from the McKean-Vlasov limit for weakly interacting diffusions
    • D.A. Dawson J. Gärtner 1987 Large deviation from the McKean-Vlasov limit for weakly interacting diffusions Stochastics 20 247 308
    • (1987) Stochastics , vol.20 , pp. 247-308
    • Dawson, D.A.1    Gärtner, J.2
  • 18
    • 84966198944 scopus 로고
    • Nonconvex minimization problems
    • I. Ekeland 1979 Nonconvex minimization problems Bull. A.M.S. (New Series) I 3 443 474
    • (1979) Bull. A.M.S. (New Series) , vol.1 , Issue.3 , pp. 443-474
    • Ekeland, I.1
  • 19
    • 0003073688 scopus 로고    scopus 로고
    • Partial differential equations and Monge-Kantorovich mass transfer
    • Evans, L.C.: Partial differential equations and Monge-Kantorovich mass transfer. Curr. Develop. in Maths. 1997
    • (1997) Curr. Develop. in Maths.
    • Evans, L.C.1
  • 20
    • 0018156010 scopus 로고
    • Exit probabilities and optimal stochastic control
    • W.H. Fleming 1978 Exit probabilities and optimal stochastic control Appl. Math. Optimiz. 4 329 346
    • (1978) Appl. Math. Optimiz. , vol.4 , pp. 329-346
    • Fleming, W.H.1
  • 23
    • 42349089599 scopus 로고    scopus 로고
    • Mathematical Surveys and Monograph, American Mathematical Society, Rhode Island
    • Feng, J., Kurtz, T.G.: Large Deviations for Stochastic Processes. Mathematical Surveys and Monograph, vol. 131. American Mathematical Society, Rhode Island, 2006
    • (2006) Large Deviations for Stochastic Processes , vol.131
    • Feng, J.1    Kurtz, T.G.2
  • 24
    • 0001103156 scopus 로고    scopus 로고
    • The geometry of optimal transportation.
    • W. Gangbo J.R. McCann 1996 The geometry of optimal transportation. Acta Math. 177 113 161
    • (1996) Acta Math. , vol.177 , pp. 113-161
    • Gangbo, W.1    McCann, J.R.2
  • 25
    • 0031116136 scopus 로고    scopus 로고
    • Phase segregation dynamics in particle systems with long range interactions. I. Macroscopic limits
    • G. Giacomin J.L. Lebowitz 1997 Phase segregation dynamics in particle systems with long range interactions. I. Macroscopic limits J. Stat. Phys. 87 37
    • (1997) J. Stat. Phys. , vol.87 , pp. 37
    • Giacomin, G.1    Lebowitz, J.L.2
  • 26
    • 0000709786 scopus 로고    scopus 로고
    • Hamilton-Jacobi-Bellman equations for the optimal control of the Duncan-Mortensen-Zakai equation
    • F. Gozzi A. Swiech 2000 Hamilton-Jacobi-Bellman equations for the optimal control of the Duncan-Mortensen-Zakai equation J. Funct. Anal. 172 2 466 510
    • (2000) J. Funct. Anal. , vol.172 , Issue.2 , pp. 466-510
    • Gozzi, F.1    Swiech, A.2
  • 27
    • 38249013039 scopus 로고
    • Viscosity solutions for a class of Hamilton-Jacobi equations in Hilbert spaces
    • H. Ishii 1992 Viscosity solutions for a class of Hamilton-Jacobi equations in Hilbert spaces J. Funct. Anal. 105 2 301 341
    • (1992) J. Funct. Anal. , vol.105 , Issue.2 , pp. 301-341
    • Ishii, H.1
  • 28
    • 0032343437 scopus 로고    scopus 로고
    • The variational formulation of the Fokker-Planck equation
    • R. Jordan D. Kinderlehrer F. Otto 1998 The variational formulation of the Fokker-Planck equation SIAM J. Math. Anal. 29 1 1 17
    • (1998) SIAM J. Math. Anal. , vol.29 , Issue.1 , pp. 1-17
    • Jordan, R.1    Kinderlehrer, D.2    Otto, F.3
  • 29
    • 0001946235 scopus 로고
    • Theory of spinodal decomposition in alloys
    • J.S. Langer 1971 Theory of spinodal decomposition in alloys Ann. Phys. 65 53
    • (1971) Ann. Phys. , vol.65 , pp. 53
    • Langer, J.S.1
  • 30
    • 0002183031 scopus 로고
    • Some properties of the viscosity semigroups for Hamilton-Jacobi equations
    • Eds. J.K. Hale and P. Martinez-Amores
    • Lions, P.L.: Some properties of the viscosity semigroups for Hamilton-Jacobi equations. Nonlinear differential equations. Pitman Research Notes in Mathematics, vol. 132 (Eds. J.K. Hale and P. Martinez-Amores), 1988
    • (1988) Nonlinear Differential Equations. Pitman Research Notes in Mathematics , vol.132
    • Lions, P.L.1
  • 31
    • 84974004014 scopus 로고
    • Existence and uniqueness of monotone measure-preserving maps
    • J.R. McCann 1995 Existence and uniqueness of monotone measure-preserving maps Duke Math. J. 80 2 309 323
    • (1995) Duke Math. J. , vol.80 , Issue.2 , pp. 309-323
    • McCann, J.R.1
  • 32
    • 0001560970 scopus 로고    scopus 로고
    • The geometry of dissipative evolution equations: The porous medium equation
    • F. Otto 2001 The geometry of dissipative evolution equations: the porous medium equation Comm. P.D.Es 26 1-2 101 174
    • (2001) Comm. P.D.Es , vol.26 , Issue.12 , pp. 101-174
    • Otto, F.1
  • 33
    • 84972545670 scopus 로고
    • Characterization of the subdifferentials of convex functions
    • R.T. Rockafellar 1966 Characterization of the subdifferentials of convex functions Pacific J. Math. 17 497 510
    • (1966) Pacific J. Math. , vol.17 , pp. 497-510
    • Rockafellar, R.T.1
  • 34
    • 84972512687 scopus 로고
    • On the generators of non-negative contraction semi-groups in Banach lattices
    • K. Sato 1968 On the generators of non-negative contraction semi-groups in Banach lattices J. Math. Soc. Japan 20 3 423 436
    • (1968) J. Math. Soc. Japan , vol.20 , Issue.3 , pp. 423-436
    • Sato, K.1
  • 35
    • 0041112426 scopus 로고
    • Accretive differential operators.
    • E. Sinestrari 1976 Accretive differential operators. Boll. U.M.I. 13 B(5 19 31
    • (1976) Boll. U.M.I. , vol.13 , Issue.B5 , pp. 19-31
    • Sinestrari, E.1
  • 36
    • 0001453735 scopus 로고
    • Optimization of functions on certain subsets of Banach spaces
    • C. Stegall 1978 Optimization of functions on certain subsets of Banach spaces Math. Ann. 236 171 176
    • (1978) Math. Ann. , vol.236 , pp. 171-176
    • Stegall, C.1
  • 38
    • 38249013207 scopus 로고
    • Viscosity solutions of Hamilton-Jacobi equations with unbounded nonlinear terms
    • D. Tataru 1992 Viscosity solutions of Hamilton-Jacobi equations with unbounded nonlinear terms J. Math. Anal. Appl. 163 2 345 392
    • (1992) J. Math. Anal. Appl. , vol.163 , Issue.2 , pp. 345-392
    • Tataru, D.1
  • 39
    • 2442557820 scopus 로고    scopus 로고
    • Graduate Studies in Mathematics, American Mathematical Society, Providence, Rhode Island
    • Villani, C.: Topics in Mass Transportation. Graduate Studies in Mathematics, vol 58. American Mathematical Society, Providence, Rhode Island, 2003
    • (2003) Topics in Mass Transportation , vol.58
    • Villani, C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.