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Volumn 46, Issue 5, 2007, Pages 1897-1921

Bolza problems with discontinuous Lagrangians and Lipschitz-continuity of the value function

Author keywords

Bolza problems; Hamilton jacobi equations; Value function

Indexed keywords

ARSENIC;

EID: 48849094215     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/060654311     Document Type: Article
Times cited : (11)

References (36)
  • 2
    • 0000467856 scopus 로고
    • Lipschitz regularity for minimizers of integral functionals with highly discontinuous integrands
    • L. AMBROSIO, O. ASCENZI, AND G. BUTTAZZO, Lipschitz regularity for minimizers of integral functionals with highly discontinuous integrands, J. Math. Anal. Appl., 142 (1989), pp. 301-316.
    • (1989) J. Math. Anal. Appl , vol.142 , pp. 301-316
    • AMBROSIO, L.1    ASCENZI, O.2    BUTTAZZO, G.3
  • 5
    • 2342491560 scopus 로고    scopus 로고
    • Large time behaviour of fronts governed by eikonal equations
    • G. BARLES AND J. M. ROQUEJOFFRE, Large time behaviour of fronts governed by eikonal equations, Interfaces Free Bound., 5 (2003), pp. 83-102.
    • (2003) Interfaces Free Bound , vol.5 , pp. 83-102
    • BARLES, G.1    ROQUEJOFFRE, J.M.2
  • 6
    • 30844470675 scopus 로고    scopus 로고
    • Monge solutions for discontinuous Hamiltonians
    • A. BRIANI AND A. DAVINI, Monge solutions for discontinuous Hamiltonians, ESAIM Control Optim. Calc. Var., 11 (2005), pp. 229-251.
    • (2005) ESAIM Control Optim. Calc. Var , vol.11 , pp. 229-251
    • BRIANI, A.1    DAVINI, A.2
  • 7
    • 0842315739 scopus 로고    scopus 로고
    • One-Dimensional Variational Problems. An Introduction
    • The Clarendon Press, Oxford University Press, New York
    • G. BUTTAZZO, M. GIAQULNTA, AND S. HILDEBRANDT, One-Dimensional Variational Problems. An Introduction, Oxford Lecture Ser. Math. Appl., 15, The Clarendon Press, Oxford University Press, New York, 1998.
    • (1998) Oxford Lecture Ser. Math. Appl , vol.15
    • BUTTAZZO, G.1    GIAQULNTA, M.2    HILDEBRANDT, S.3
  • 8
    • 0040059911 scopus 로고    scopus 로고
    • On viscosity solutions of fully nonlinear equations with measurable ingredients
    • L. CAFFARELLI, M. G. CRANDALL, M. KOCAN, AND A. SWIECH, On viscosity solutions of fully nonlinear equations with measurable ingredients, Comm. Pure Appl. Math., 49 (1996), pp. 365-397.
    • (1996) Comm. Pure Appl. Math , vol.49 , pp. 365-397
    • CAFFARELLI, L.1    CRANDALL, M.G.2    KOCAN, M.3    SWIECH, A.4
  • 9
    • 52649160654 scopus 로고    scopus 로고
    • Lax-type formulas for time-dependent measurable Hamilton-Jacobi equations
    • in preparation
    • F. CAMILLI, A. DAVINI, AND A. SICONOLFI, Lax-type formulas for time-dependent measurable Hamilton-Jacobi equations, in preparation.
    • CAMILLI, F.1    DAVINI, A.2    SICONOLFI, A.3
  • 10
    • 2342466049 scopus 로고    scopus 로고
    • An Hopf-Lax formula for a class of measurable Hamilton-Jacobi equations
    • F. CAMILLI, An Hopf-Lax formula for a class of measurable Hamilton-Jacobi equations, Nonlinear Anal., 57 (2004), pp. 265-286.
    • (2004) Nonlinear Anal , vol.57 , pp. 265-286
    • CAMILLI, F.1
  • 11
    • 2342496261 scopus 로고    scopus 로고
    • Hamilton-Jacobi equations with measurable dependence on the state variable
    • F. CAMILLI AND A. SICONOLFI, Hamilton-Jacobi equations with measurable dependence on the state variable, Adv. Differential Equations, 8 (2003), pp. 733-768.
    • (2003) Adv. Differential Equations , vol.8 , pp. 733-768
    • CAMILLI, F.1    SICONOLFI, A.2
  • 13
    • 33750184121 scopus 로고    scopus 로고
    • Effective Hamiltonian and homogenization of measurable eikonal equations
    • F. CAMILLI AND A. SICONOLFI, Effective Hamiltonian and homogenization of measurable eikonal equations, Arch. Ration. Mech. Anal., 183 (2007), pp. 1-20.
    • (2007) Arch. Ration. Mech. Anal , vol.183 , pp. 1-20
    • CAMILLI, F.1    SICONOLFI, A.2
  • 17
    • 84966256938 scopus 로고
    • Regularity properties of solutions to the basic problem in the calculus of variations
    • F. H. CLARKE AND R. B. VINTER, Regularity properties of solutions to the basic problem in the calculus of variations, Trans. Amer. Math. Soc., 289 (1985), pp. 73-98.
    • (1985) Trans. Amer. Math. Soc , vol.289 , pp. 73-98
    • CLARKE, F.H.1    VINTER, R.B.2
  • 18
    • 11944253919 scopus 로고    scopus 로고
    • Autonomous integral functionals with discontinuous nonconvex integrands: Lipschitz regularity of minimizers, DuBois-Reymond necessary conditions, and Hamilton-Jacobi equations
    • G. DAL MASO AND H. FRANKOWSKA, Autonomous integral functionals with discontinuous nonconvex integrands: Lipschitz regularity of minimizers, DuBois-Reymond necessary conditions, and Hamilton-Jacobi equations, Appl. Math. Optim., 48 (2003), pp. 39-66.
    • (2003) Appl. Math. Optim , vol.48 , pp. 39-66
    • DAL MASO, G.1    FRANKOWSKA, H.2
  • 19
    • 0034425672 scopus 로고    scopus 로고
    • Value functions for Bolza problems with discontinuous Lagrangians and Hamilton-Jacobi inequalities
    • G. DAL MASO AND H. FRANKOWSKA, Value functions for Bolza problems with discontinuous Lagrangians and Hamilton-Jacobi inequalities, ESAIM Control Optim. Calc. Var., 5 (2000), pp. 369-393.
    • (2000) ESAIM Control Optim. Calc. Var , vol.5 , pp. 369-393
    • DAL MASO, G.1    FRANKOWSKA, H.2
  • 20
    • 52649120179 scopus 로고    scopus 로고
    • Integral representation of abstract functionals of autonomous type
    • to appear
    • A. DAVINI, Integral representation of abstract functionals of autonomous type, Proc. Roy. Soc. Edinburgh Sect. A, to appear.
    • Proc. Roy. Soc. Edinburgh Sect. A
    • DAVINI, A.1
  • 21
    • 33947248437 scopus 로고    scopus 로고
    • A generalized dynamical approach to the large time behavior of solutions of Hamilton-Jacobi equations
    • A. DAVINI AND A. SICONOLFI, A generalized dynamical approach to the large time behavior of solutions of Hamilton-Jacobi equations, SIAM J. Math. Anal., 38 (2006), pp. 478-502.
    • (2006) SIAM J. Math. Anal , vol.38 , pp. 478-502
    • DAVINI, A.1    SICONOLFI, A.2
  • 22
    • 11944264666 scopus 로고    scopus 로고
    • PDE aspects of Aubry-Mather theory for continuous convex Hamiltonians
    • A. FATHI AND A. SICONOLFI, PDE aspects of Aubry-Mather theory for continuous convex Hamiltonians, Calc. Var. Partial Differential Equations, 22 (2005), pp. 185-228.
    • (2005) Calc. Var. Partial Differential Equations , vol.22 , pp. 185-228
    • FATHI, A.1    SICONOLFI, A.2
  • 23
    • 0034458920 scopus 로고    scopus 로고
    • Extended Hamilton-Jacobi characterization of value functions in optimal control
    • G. N. GALBRAITH, Extended Hamilton-Jacobi characterization of value functions in optimal control, SIAM J. Control Optim., 39 (2000), pp. 281-305.
    • (2000) SIAM J. Control Optim , vol.39 , pp. 281-305
    • GALBRAITH, G.N.1
  • 25
    • 0001756668 scopus 로고
    • On the lower semicontinuity of integral functionals
    • A. D. IOFFE, On the lower semicontinuity of integral functionals. I, SIAM J. Control Optim., 15 (1977), pp. 521-538.
    • (1977) I, SIAM J. Control Optim , vol.15 , pp. 521-538
    • IOFFE, A.D.1
  • 26
    • 0004232356 scopus 로고
    • Res. Notes in Math. 69, Pitman Advanced Publishing Program, Boston, MA, London
    • P. L. LIONS, Generalized Solutions of Hamilton-Jacobi Equations, Res. Notes in Math. 69, Pitman (Advanced Publishing Program), Boston, MA, London, 1982.
    • (1982) Generalized Solutions of Hamilton-Jacobi Equations
    • LIONS, P.L.1
  • 27
    • 0039799153 scopus 로고    scopus 로고
    • The "hump" effect in solid propellant combustion
    • G. NAMAH AND J. M. ROQUEJOFFRE, The "hump" effect in solid propellant combustion, Interfaces Free Bound., 2 (2000), pp. 449-467.
    • (2000) Interfaces Free Bound , vol.2 , pp. 449-467
    • NAMAH, G.1    ROQUEJOFFRE, J.M.2
  • 28
    • 0000695344 scopus 로고
    • Eikonal equations with discontinuities
    • R. T. NEWCOMB AND J. Su, Eikonal equations with discontinuities, Differential Integral Equations, 8 (1995), pp. 1947-1960.
    • (1995) Differential Integral Equations , vol.8 , pp. 1947-1960
    • NEWCOMB, R.T.1    Su, J.2
  • 29
    • 0016952427 scopus 로고
    • Weak lower semicontinuity of integral functionals. Existence theorem issue
    • C. OLECH, Weak lower semicontinuity of integral functionals. Existence theorem issue, J. Optim. Theory Appl., 19 (1976), pp. 3-16.
    • (1976) J. Optim. Theory Appl , vol.19 , pp. 3-16
    • OLECH, C.1
  • 30
    • 0037053703 scopus 로고    scopus 로고
    • Solutions of Hamilton-Jacobi equations and scalar conservation laws with discontinuous space-time dependence
    • D. OSTROV, Solutions of Hamilton-Jacobi equations and scalar conservation laws with discontinuous space-time dependence, J. Differential Equations, 182 (2002), pp. 51-77.
    • (2002) J. Differential Equations , vol.182 , pp. 51-77
    • OSTROV, D.1
  • 31
    • 0003346020 scopus 로고
    • Convex Analysis
    • Princeton University Press, Princeton, NJ
    • R. T. ROCKAFELLAR, Convex Analysis, Princeton Mathematical Series 28, Princeton University Press, Princeton, NJ, 1970.
    • (1970) Princeton Mathematical Series , vol.28
    • ROCKAFELLAR, R.T.1
  • 32
    • 0004258516 scopus 로고    scopus 로고
    • Grundlehren Math. Wiss, Fundamental Principles of Mathematical Sciences] 317, Springer-Verlag, Berlin
    • R. T. ROCKAFELLAR AND R. J.-B. WETS, Variational Analysis, Grundlehren Math. Wiss. [Fundamental Principles of Mathematical Sciences] 317, Springer-Verlag, Berlin, 1998.
    • (1998) Variational Analysis
    • ROCKAFELLAR, R.T.1    WETS, R.J.-B.2
  • 33
    • 0036059914 scopus 로고    scopus 로고
    • Boundary value problems for Hamilton-Jacobi equations with discontinuous Lagrangian
    • P. SORAVIA, Boundary value problems for Hamilton-Jacobi equations with discontinuous Lagrangian, Indiana Univ. Math. J., 51 (2002), pp. 451-477.
    • (2002) Indiana Univ. Math. J , vol.51 , pp. 451-477
    • SORAVIA, P.1
  • 34
    • 0346307635 scopus 로고    scopus 로고
    • On viscosity solutions of irregular Hamilton-Jacobi equations
    • T. STRÖMBERG, On viscosity solutions of irregular Hamilton-Jacobi equations, Arch. Math. (Basel) 81 (2003), pp. 678-688.
    • (2003) Arch. Math. (Basel) , vol.81 , pp. 678-688
    • STRÖMBERG, T.1
  • 35
    • 54249096254 scopus 로고
    • Sur une méthode directe du calcul des variations
    • L. TONELLI, Sur une méthode directe du calcul des variations, Rend. Circ. Mat. Palermo, 39 (1915), pp. 223-264.
    • (1915) Rend. Circ. Mat. Palermo , vol.39 , pp. 223-264
    • TONELLI, L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.