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Volumn 54, Issue 1, 2015, Pages 539-572

Regularity results and large time behavior for integro-differential equations with coercive Hamiltonians

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EID: 84939465817     PISSN: 09442669     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00526-014-0794-x     Document Type: Article
Times cited : (23)

References (34)
  • 1
    • 0030351484 scopus 로고    scopus 로고
    • Viscosity solutions of nonlinear integro-differential equations
    • Alvarez, O., Tourin, A.: Viscosity solutions of nonlinear integro-differential equations. Annales de L’I.H.P., section C 13(3), 293–317 (1996)
    • (1996) Annales de L’I.H.P., section C , vol.13 , Issue.3 , 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., Da Lio, F.: On the strong maximum principle for fully nonlinear degenerate elliptic equations. Arch. Math. (Basel) 73(4), 276–285 (1999)
    • (1999) Arch. Math. (Basel) , vol.73 , Issue.4 , pp. 276-285
    • Bardi, M.1    Da Lio, F.2
  • 3
    • 85018094844 scopus 로고
    • Solutions de Viscosite des Equations de Hamilton–Jacobi Collection “Mathematiques et Applications” de la SIAM, no 17
    • Barles, G.: Solutions de Viscosite des Equations de Hamilton–Jacobi Collection “Mathematiques et Applications” de la SIAM, no 17. Springer (1994)
    • (1994) Springer
    • Barles, G.1
  • 4
    • 77955420247 scopus 로고    scopus 로고
    • A short proof of the C0,α- regularity of viscosity subsolutions for superquadratic viscous Hamilton–Jacobi equations and applications
    • Barles, G.: A short proof of the C0,α- regularity of viscosity subsolutions for superquadratic viscous Hamilton–Jacobi equations and applications. Nonlinear Anal. 73, 31–47 (2010)
    • (2010) Nonlinear Anal , vol.73 , pp. 31-47
    • Barles, G.1
  • 5
    • 84859644236 scopus 로고    scopus 로고
    • Lipschitz regularity of solutions for mixed integro-differential equations
    • Barles, G., Chasseigne, E., Ciomaga, A., Imbert, C.: Lipschitz regularity of solutions for mixed integro-differential equations. J. Differ. Equ. 252, 6012–6060 (2012)
    • (2012) J. Differ. Equ , vol.252 , pp. 6012-6060
    • Barles, G.1    Chasseigne, E.2    Ciomaga, A.3    Imbert, C.4
  • 6
    • 84899437010 scopus 로고    scopus 로고
    • Time behavior of periodic viscosity solutions for uniformly parabolic integro-differential equations
    • Barles, G., Chasseigne, E., Ciomaga, A., Imbert, C.: Time behavior of periodic viscosity solutions for uniformly parabolic integro-differential equations. Calc. Var. Partial Differ. Equ. 50(1–2), 283–304 (2014)
    • (2014) Calc. Var. Partial Differ. Equ , vol.50 , Issue.1-2 , pp. 283-304
    • Barles, G.1    Chasseigne, E.2    Ciomaga, A.3    Imbert, C.4
  • 7
    • 84924786948 scopus 로고    scopus 로고
    • On Neumann type problems for nonlocal equations set in a half space
    • Barles, G., Chasseigne, E., Georgelin, C., Jakobsen, E.: On Neumann type problems for nonlocal equations set in a half space. Trans. Am. Math. Soc. 366(9), 4873–4917 (2014)
    • (2014) Trans. Am. Math. Soc , vol.366 , Issue.9 , pp. 4873-4917
    • Barles, G.1    Chasseigne, E.2    Georgelin, C.3    Jakobsen, E.4
  • 8
    • 42549114402 scopus 로고    scopus 로고
    • On the Dirichlet problem for second-order elliptic integro-differential equations. Indiana Univ
    • Barles, G., Chasseigne, E., Imbert, C.: On the Dirichlet problem for second-order elliptic integro-differential equations. Indiana Univ. Math. J. 57(1), 213–246 (2008)
    • (2008) Math. J , vol.57 , Issue.1 , pp. 213-246
    • Barles, G.1    Chasseigne, E.2    Imbert, C.3
  • 9
    • 43049183444 scopus 로고    scopus 로고
    • Second-order eliptic integro-differential equations: viscosity solutions’ theory revisited
    • Barles, G., Imbert, C.: Second-order eliptic integro-differential equations: viscosity solutions’ theory revisited. IHP Anal. Non Linéare 25(3), 567–585 (2008)
    • (2008) IHP Anal. Non Linéare , vol.25 , Issue.3 , pp. 567-585
    • Barles, G.1    Imbert, C.2
  • 10
    • 0035541168 scopus 로고    scopus 로고
    • Space-time periodic solutions and long-time behavior of solutions of quasilinear parabolic equations
    • Barles, G., Souganidis, P.E.: Space-time periodic solutions and long-time behavior of solutions of quasilinear parabolic equations. SIAM J. Math. Anal. 32, 1311–1323 (2001)
    • (2001) SIAM J. Math. Anal , vol.32 , pp. 1311-1323
    • Barles, G.1    Souganidis, P.E.2
  • 12
    • 68049121967 scopus 로고    scopus 로고
    • Regularity theory for nonlocal integro-differential equations
    • Caffarelli, L., Silvestre, L.: Regularity theory for nonlocal integro-differential equations. Commun. Pure Appl. Math. 62(5), 597–638 (2009)
    • (2009) Commun. Pure Appl. Math , vol.62 , Issue.5 , pp. 597-638
    • Caffarelli, L.1    Silvestre, L.2
  • 13
    • 77952042519 scopus 로고    scopus 로고
    • Hölder estimates for degenerate elliptic equations with coercive Hamiltonians
    • Capuzzo-Dolcetta, I., Leoni, F., Porretta, A.: Hölder estimates for degenerate elliptic equations with coercive Hamiltonians. Trans. Am. Math. Soc. 362(9), 4511–4536 (2010)
    • (2010) Trans. Am. Math. Soc , vol.362 , Issue.9 , pp. 4511-4536
    • Capuzzo-Dolcetta, I.1    Leoni, F.2    Porretta, A.3
  • 14
    • 77952507525 scopus 로고    scopus 로고
    • Hölder estimates in space-time for viscosity solutions of Hamilton–Jacobi equations
    • Cardaliaguet, P., Cannarsa, P.: Hölder estimates in space-time for viscosity solutions of Hamilton–Jacobi equations. CPAM 63(5), 590–629 (2010)
    • (2010) CPAM , vol.63 , Issue.5 , pp. 590-629
    • Cardaliaguet, P.1    Cannarsa, P.2
  • 15
    • 79957448501 scopus 로고    scopus 로고
    • Höder regularity for viscosity solutions of fully nonlinear, local or nonlocal, Hamilton–Jacobi equations with superquadratic growth in the gradient
    • Cardaliaguet, P., Rainer, C.: Höder regularity for viscosity solutions of fully nonlinear, local or nonlocal, Hamilton–Jacobi equations with superquadratic growth in the gradient. SIAM J. Control Optim. 49(2), 555–573 (2011)
    • (2011) SIAM J. Control Optim , vol.49 , Issue.2 , pp. 555-573
    • Cardaliaguet, P.1    Rainer, C.2
  • 16
    • 42549106730 scopus 로고    scopus 로고
    • The Dirichlet problem for some nonlocal diffusion equations
    • Chasseigne, E.: The Dirichlet problem for some nonlocal diffusion equations. Differ. Integr. Equ. 20(12), 1389–1404 (2007)
    • (2007) Differ. Integr. Equ , vol.20 , Issue.12 , pp. 1389-1404
    • Chasseigne, E.1
  • 17
    • 84883759137 scopus 로고    scopus 로고
    • On the strong maximum principle for second order nonlinear parabolic integro-differential equations
    • Ciomaga, A.: On the strong maximum principle for second order nonlinear parabolic integro-differential equations. Adv. Differ. Equ. 17, 635–671 (2012)
    • (2012) Adv. Differ. Equ , vol.17 , pp. 635-671
    • Ciomaga, A.1
  • 18
    • 34249889875 scopus 로고    scopus 로고
    • Maximum principles, sliding techniques and applications to nonlocal equations
    • Coville, J.: Maximum principles, sliding techniques and applications to nonlocal equations. Electron. J. Differ. Equ. 2007(68), 1–23 (2007)
    • (2007) Electron. J. Differ. Equ , vol.2007 , Issue.68 , pp. 1-23
    • Coville, J.1
  • 19
    • 44349194901 scopus 로고    scopus 로고
    • Remarks on the strong maximum principle for nonlocal operators
    • Coville, J.: Remarks on the strong maximum principle for nonlocal operators. Electron. J. Differ. Equ. 66, 1–10 (2008)
    • (2008) Electron. J. Differ. Equ , vol.66 , pp. 1-10
    • Coville, J.1
  • 20
    • 84967708673 scopus 로고
    • User’s guide to viscosity solutions of second order partial differential equations
    • Crandall, M.G., Ishii, H., Lions, P.-L.: User’s guide to viscosity solutions of second order partial differential equations. Bull. Am. Math. Soc. (N.S.) 27(1), 1–67 (1992)
    • (1992) Bull. Am. Math. Soc. (N.S.) , vol.27 , Issue.1 , pp. 1-67
    • Crandall, M.G.1    Ishii, H.2    Lions, P.-L.3
  • 21
    • 0036383354 scopus 로고    scopus 로고
    • Comparison results for quasilinear equations in annular domains and applications
    • Da Lio, F.: Comparison results for quasilinear equations in annular domains and applications. Commun. Partial Differ. Equ. 27(1 & 2), 283–323 (2002)
    • (2002) Commun. Partial Differ. Equ , vol.27 , Issue.1-2 , pp. 283-323
    • Da Lio, F.1
  • 22
    • 84863469913 scopus 로고    scopus 로고
    • Hitchhiker’s guide to the fractional Sobolev spaces
    • Di Neza, E., Palatucci, G., Valdinoci, E.: Hitchhiker’s guide to the fractional Sobolev spaces. Bull. Sci. Math. 136(5), 521–573 (2012)
    • (2012) Bull. Sci. Math , vol.136 , Issue.5 , pp. 521-573
    • Di Neza, E.1    Palatucci, G.2    Valdinoci, E.3
  • 23
    • 0003523792 scopus 로고
    • Dirichlet forms and symmetric Markov processes. de Grueter Stud
    • Fukushima, M., Oshima, Y., Takeda, M.: Dirichlet forms and symmetric Markov processes. de Grueter Stud. Math. 19 (1994)
    • (1994) Math , pp. 19
    • Fukushima, M.1    Oshima, Y.2    Takeda, M.3
  • 24
    • 33746215057 scopus 로고    scopus 로고
    • The integration by part of the regional fractional Laplacian
    • Guan, Q.Y.: The integration by part of the regional fractional Laplacian. Commun. Math. Phys. 266, 289–329 (2006)
    • (2006) Commun. Math. Phys , vol.266 , pp. 289-329
    • Guan, Q.Y.1
  • 25
    • 32044448718 scopus 로고    scopus 로고
    • Reflected symmetric α stable process and regional fractional Laplacian
    • Guan, Q.Y., Ma, Z.M.: Reflected symmetric α stable process and regional fractional Laplacian. Probab. Theory Relat. Fields 134, 649–694 (2006)
    • (2006) Probab. Theory Relat. Fields , vol.134 , pp. 649-694
    • Guan, Q.Y.1    Ma, Z.M.2
  • 26
    • 0000692544 scopus 로고
    • Existence and uniqueness of solutions of Hamilton–Jacobi equations
    • Ishii, H.: Existence and uniqueness of solutions of Hamilton–Jacobi equations. Funkcialaj Ekvacioj 29, 167–188 (1986)
    • (1986) Funkcialaj Ekvacioj , vol.29 , pp. 167-188
    • Ishii, H.1
  • 27
    • 77949774164 scopus 로고    scopus 로고
    • A class of integral equations and approximation of p-Laplace equations
    • Ishii, H., Nakamura, G.: A class of integral equations and approximation of p-Laplace equations. Calc. Var. Partial Differ. Equ. 37(3–4), 485–522 (2010)
    • (2010) Calc. Var. Partial Differ. Equ , vol.37 , Issue.3-4 , pp. 485-522
    • Ishii, H.1    Nakamura, G.2
  • 29
    • 33750631446 scopus 로고    scopus 로고
    • Weak convergence of censored and reflected stable processes
    • Kim, P.: Weak convergence of censored and reflected stable processes. Stoch. Process. Appl. 116(12), 1792–1814 (2006)
    • (2006) Stoch. Process. Appl , vol.116 , Issue.12 , pp. 1792-1814
    • Kim, P.1
  • 30
    • 12744266484 scopus 로고    scopus 로고
    • A beginner’s guide to the theory of viscosity solutions
    • Mathematical Society of, Japan, Tokyo
    • Koike, S.: A beginner’s guide to the theory of viscosity solutions. MSJ Memoirs, vol. 13. Mathematical Society of Japan, Tokyo (2004)
    • (2004) MSJ Memoirs , vol.13
    • Koike, S.1
  • 31
    • 84949351553 scopus 로고
    • Équations d’Hamilton–Jacobi du emier Ordre Avec Termes Intégro-Différentiels. I. Unicité des solutions de viscosité
    • Sayah, A.: Équations d’Hamilton–Jacobi du emier Ordre Avec Termes Intégro-Différentiels. I. Unicité des solutions de viscosité. Commun. Partial Differ. Equ. 16, 1057–1074 (1991)
    • (1991) Commun. Partial Differ. Equ , vol.16 , pp. 1057-1074
    • Sayah, A.1
  • 32
    • 84949338341 scopus 로고
    • Équations d’Hamilton–Jacobi du emier Ordre Avec Termes Intégro-Différentiels. II. Existence de solutions de viscosité
    • Sayah, A.: Équations d’Hamilton–Jacobi du emier Ordre Avec Termes Intégro-Différentiels. II. Existence de solutions de viscosité. Commun. Partial Differ. Equ. 16, 1075–1093 (1991)
    • (1991) Commun. Partial Differ. Equ , vol.16 , pp. 1075-1093
    • Sayah, A.1
  • 33
    • 77950256730 scopus 로고    scopus 로고
    • Large time behavior of solutions of viscous Hamilton–Jacobi equations with superquadratic Hamiltonian
    • Tchamba, T.T.: Large time behavior of solutions of viscous Hamilton–Jacobi equations with superquadratic Hamiltonian. Asymptot. Anal. 66, 161–186 (2010)
    • (2010) Asymptot. Anal , vol.66 , pp. 161-186
    • Tchamba, T.T.1
  • 34
    • 84903384507 scopus 로고    scopus 로고
    • Existence and uniqueness for integro-differential equations with dominating drift terms
    • Topp, E.: Existence and uniqueness for integro-differential equations with dominating drift terms. Commun. Partial Differ. Equ. 39(8), 1523–1554 (2014)
    • (2014) Commun. Partial Differ. Equ , vol.39 , Issue.8 , pp. 1523-1554
    • Topp, E.1


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