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Volumn 30, Issue 2, 2017, Pages 703-734

Lipschitz regularity for integro-differential equations with coercive Hamiltonians and application to large time behavior

Author keywords

integro differential equations; large time behavior; Lipschitz regularity; nonlinear PDEs

Indexed keywords


EID: 85011347294     PISSN: 09517715     EISSN: 13616544     Source Type: Journal    
DOI: 10.1088/1361-6544/aa527f     Document Type: Article
Times cited : (21)

References (31)
  • 1
    • 0030351484 scopus 로고    scopus 로고
    • Viscosity solutions of nonlinear integro-differential equations
    • Alvarez O and Tourin A 1996 Viscosity solutions of nonlinear integro-differential equations Ann. Inst. Henri Poincaré 13 293-317
    • (1996) Ann. Inst. Henri Poincaré , vol.13 , pp. 293-317
    • Alvarez, O.1    Tourin, A.2
  • 2
    • 0033247049 scopus 로고    scopus 로고
    • On the strong maximum principle for fully nonlinear degenerate elliptic equations
    • Bardi M and Da Lio F 1999 On the strong maximum principle for fully nonlinear degenerate elliptic equations Arch. Math 73 276-85
    • (1999) Arch. Math , vol.73 , pp. 276-285
    • Bardi, M.1    Da Lio, F.2
  • 3
  • 4
    • 77955420247 scopus 로고    scopus 로고
    • A Short Proof if the C0,σ-regularity of viscosity subsolutions for superquadratic viscous Hamilton-Jacobi equations and applications
    • Barles G 2010 A Short Proof if the C0,σ-regularity of viscosity subsolutions for superquadratic viscous Hamilton-Jacobi equations and applications Nonlinear Anal. 73 31-47
    • (2010) Nonlinear Anal. , vol.73 , pp. 31-47
    • Barles, G.1
  • 5
    • 84972503006 scopus 로고
    • A weak Bernstein method for fully nonlinear elliptic equations
    • Barles G 1991 A weak Bernstein method for fully nonlinear elliptic equations Differ. Integral Equ. 4 241-62
    • (1991) Differ. Integral Equ. , vol.4 , pp. 241-262
    • Barles, G.1
  • 6
    • 78650409141 scopus 로고    scopus 로고
    • Hölder continuity of solutions of second-order non-linear elliptic integro-differential equations
    • Barles G, Chasseigne E and Imbert C 2011 Hölder continuity of solutions of second-order non-linear elliptic integro-differential equations J. Eur. Math. Soc. 13 1-26
    • (2011) J. Eur. Math. Soc. , vol.13 , pp. 1-26
    • Barles, G.1    Chasseigne, E.2    Imbert, C.3
  • 7
    • 84859644236 scopus 로고    scopus 로고
    • Lipschitz regularity of solutions for mixed integro-differential equations
    • Barles G, Chasseigne E, Ciomaga A and Imbert C 2012 Lipschitz regularity of solutions for mixed integro-differential equations J. Differ. Equ. 252 6012-60
    • (2012) J. Differ. Equ. , vol.252 , pp. 6012-6060
    • Barles, G.1    Chasseigne, E.2    Ciomaga, A.3    Imbert, C.4
  • 8
    • 84899437010 scopus 로고    scopus 로고
    • Large time behavior of periodic viscosity solutions for uniformly parabolic integro-differential equations
    • Barles G, Chasseigne E, Ciomaga A and Imbert C 2014 Large time behavior of periodic viscosity solutions for uniformly parabolic integro-differential equations Calc. Var. PDE 50 283-304
    • (2014) Calc. Var. PDE , vol.50 , pp. 283-304
    • Barles, G.1    Chasseigne, E.2    Ciomaga, A.3    Imbert, C.4
  • 9
    • 43049183444 scopus 로고    scopus 로고
    • Second-order eliptic integro-differential equations: Viscosity solutions' theory revisited
    • Barles G and Imbert C 2008 Second-order eliptic integro-differential equations: viscosity solutions' theory revisited Ann. Inst. Henri Poincaré 25 567-85
    • (2008) Ann. Inst. Henri Poincaré , vol.25 , pp. 567-585
    • Barles, G.1    Imbert, C.2
  • 10
    • 84939465817 scopus 로고    scopus 로고
    • Regularity results and large time behavior for integro-differential equations with coercive Hamiltonians
    • Barles G, Koike S, Ley O and Topp E 2015 Regularity results and large time behavior for integro-differential equations with coercive Hamiltonians Calc. Var. PDE 54 539-72
    • (2015) Calc. Var. PDE , vol.54 , pp. 539-572
    • Barles, G.1    Koike, S.2    Ley, O.3    Topp, E.4
  • 11
    • 0024070155 scopus 로고
    • Exit time problems in optimal control and vanishing viscosity method
    • Barles G and Perthame B 1988 Exit time problems in optimal control and vanishing viscosity method SIAM J. Control Optim. 26 1133-48
    • (1988) SIAM J. Control Optim. , vol.26 , pp. 1133-1148
    • Barles, G.1    Perthame, B.2
  • 12
    • 0034347336 scopus 로고    scopus 로고
    • On the large time behavior of solutions of Hamilton-Jacobi equations
    • Barles G and Souganidis P E 2000 On the large time behavior of solutions of Hamilton-Jacobi equations SIAM J. Math. Anal. 31 925-39
    • (2000) SIAM J. Math. Anal. , vol.31 , pp. 925-939
    • Barles, G.1    Souganidis, P.E.2
  • 13
    • 0035541168 scopus 로고    scopus 로고
    • Space-time periodic solutions and long-time behavior of solutions of quasilinear parabolic equations
    • (electronic)
    • Barles G and Souganidis P E 2001 Space-time periodic solutions and long-time behavior of solutions of quasilinear parabolic equations SIAM J. Math. Anal. 32 1311-23 (electronic)
    • (2001) SIAM J. Math. Anal. , vol.32 , pp. 1311-1323
    • Barles, G.1    Souganidis, P.E.2
  • 14
    • 84965069898 scopus 로고    scopus 로고
    • Existence, uniqueness and asymptotic behavior for nonlocal parabolic problems with dominating gradient terms
    • Barles G and Topp E 2016 Existence, uniqueness and asymptotic behavior for nonlocal parabolic problems with dominating gradient terms SIAM J. Math. Anal. 48 1512-47
    • (2016) SIAM J. Math. Anal. , vol.48 , pp. 1512-1547
    • Barles, G.1    Topp, E.2
  • 15
    • 84948572774 scopus 로고    scopus 로고
    • Lipschitz regularity for censored subdiffusive integro-differential equations with superfractional gradient terms
    • Barles G and Topp E 2016 Lipschitz regularity for censored subdiffusive integro-differential equations with superfractional gradient terms Nonlinear Anal. 131 3-31
    • (2016) Nonlinear Anal. , vol.131 , pp. 3-31
    • Barles, G.1    Topp, E.2
  • 16
    • 0013024371 scopus 로고
    • Sur la généralisation du probléme de Dirichlet, i
    • Bernstein S 1906 Sur la généralisation du probléme de Dirichlet, I Math. Ann. 62 253-71
    • (1906) Math. Ann. , vol.62 , pp. 253-271
    • Bernstein, S.1
  • 17
    • 0002098825 scopus 로고
    • Sur la généralisation du probléme de Dirichlet, i
    • Bernstein S 1910 Sur la généralisation du probléme de Dirichlet, I Math. Ann. 69 82-136
    • (1910) Math. Ann. , vol.69 , pp. 82-136
    • Bernstein, S.1
  • 18
    • 77952042519 scopus 로고    scopus 로고
    • Hölder estimates for degenerate elliptic equations with coercive hamiltonians
    • Capuzzo-Dolcetta I, Leoni F and Porretta A 2010 Hölder estimates for degenerate elliptic equations with coercive hamiltonians Trans. Am. Math. Soc. 362 4511-36
    • (2010) Trans. Am. Math. Soc. , vol.362 , pp. 4511-4536
    • Capuzzo-Dolcetta, I.1    Leoni, F.2    Porretta, A.3
  • 19
    • 84883759137 scopus 로고    scopus 로고
    • On the strong maximum principle for second order nonlinear parabolic integro-differential equations
    • Ciomaga A 2012 On the strong maximum principle for second order nonlinear parabolic integro-differential equations Adv. Differ. Equ. 17 635-71
    • (2012) Adv. Differ. Equ. , vol.17 , pp. 635-671
    • Ciomaga, A.1
  • 20
    • 34249889875 scopus 로고    scopus 로고
    • Maximum principles, sliding techniques and applications to nonlocal equations
    • 2007
    • Coville J 2007 Maximum principles, sliding techniques and applications to nonlocal equations Electron. J. Differ. Equ. 2007 1-23
    • (2007) Electron. J. Differ. Equ. , vol.2007 , pp. 1-23
    • Coville, J.1
  • 21
    • 44349194901 scopus 로고    scopus 로고
    • Remarks on the strong maximum principle for nonlocal operators
    • Coville J 2008 Remarks on the strong maximum principle for nonlocal operators Electron. J. Differ. Equ. 66 1-10
    • (2008) Electron. J. Differ. Equ. , vol.66 , pp. 1-10
    • Coville, J.1
  • 22
    • 84967708673 scopus 로고
    • User's guide to viscosity solutions of second order partial differential equations
    • Crandall M G, Ishii H and Lions P-L 1992 User's guide to viscosity solutions of second order partial differential equations Bull. Am. Math. Soc. 27 1-67
    • (1992) Bull. Am. Math. Soc. , vol.27 , pp. 1-67
    • Crandall, M.G.1    Ishii, H.2    Lions, P.-L.3
  • 23
    • 0036383354 scopus 로고    scopus 로고
    • Comparison results for quasilinear equations in annular domains and applications
    • Da Lio F 2002 Comparison results for quasilinear equations in annular domains and applications Commun. PDE 27 283-323
    • (2002) Commun. PDE , vol.27 , pp. 283-323
    • Da Lio, F.1
  • 24
    • 84863469913 scopus 로고    scopus 로고
    • Hitchhiker's guide to the fractional sobolev spaces
    • Di Neza E, Palatucci G and Valdinoci E 2012 Hitchhiker's guide to the fractional sobolev spaces Bull. Sci. Math. 136 521-73
    • (2012) Bull. Sci. Math. , vol.136 , pp. 521-573
    • Di Neza, E.1    Palatucci, G.2    Valdinoci, E.3
  • 25
    • 84962850107 scopus 로고    scopus 로고
    • Entire solutions of fully nonlinear elliptic equations with a superlinear gradient term
    • Galise G, Koike S, Ley O and Vitolo A 2016 Entire solutions of fully nonlinear elliptic equations with a superlinear gradient term J. Math. Anal. Appl. 441 194-210
    • (2016) J. Math. Anal. Appl. , vol.441 , pp. 194-210
    • Galise, G.1    Koike, S.2    Ley, O.3    Vitolo, A.4
  • 27
    • 84990575194 scopus 로고
    • On uniqueness and existence of viscosity solutions of fully nonlinear second-order elliptic PDEs
    • Ishii H 1989 On uniqueness and existence of viscosity solutions of fully nonlinear second-order elliptic PDEs Comm. Pure Appl. Math. 42 15-45
    • (1989) Comm. Pure Appl. Math. , vol.42 , pp. 15-45
    • Ishii, H.1
  • 28
    • 0002824461 scopus 로고
    • Viscosity solutions of fully nonlinear second-order elliptic partial differential equations
    • Ishii H and Lions P L 1990 Viscosity solutions of fully nonlinear second-order elliptic partial differential equations J. Differ. Equ. 83 26-78
    • (1990) J. Differ. Equ. , vol.83 , pp. 26-78
    • Ishii, H.1    Lions, P.L.2
  • 29
    • 33646945027 scopus 로고
    • The maximum principle for viscosity solutions of fully nonlinear second order partial differential equations
    • Jensen R 1988 The maximum principle for viscosity solutions of fully nonlinear second order partial differential equations Arch. Ration. Mech. Anal. 101 1-27
    • (1988) Arch. Ration. Mech. Anal. , vol.101 , pp. 1-27
    • Jensen, R.1
  • 30
    • 84944810383 scopus 로고    scopus 로고
    • Gradient bounds for nonlinear degenerate parabolic equations and application to large time behavior of systems
    • Ley O and Nguyen V D 2016 Gradient bounds for nonlinear degenerate parabolic equations and application to large time behavior of systems Nonlinear Anal. 130 76-101
    • (2016) Nonlinear Anal. , vol.130 , pp. 76-101
    • Ley, O.1    Nguyen, V.D.2
  • 31
    • 77950256730 scopus 로고    scopus 로고
    • Large time behavior of solutions of viscous Hamilton-Jacobi equations with superquadratic Hamiltonian
    • Tchamba T T 2010 Large time behavior of solutions of viscous Hamilton-Jacobi equations with superquadratic Hamiltonian Asymptot. Anal. 66 161-86
    • (2010) Asymptot. Anal. , vol.66 , pp. 161-186
    • Tchamba, T.T.1


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