메뉴 건너뛰기




Volumn 206, Issue 1, 2012, Pages 111-157

Aleksandrov-Bakelman-Pucci Type Estimates for Integro-Differential Equations

Author keywords

[No Author keywords available]

Indexed keywords


EID: 84866415556     PISSN: 00039527     EISSN: 14320673     Source Type: Journal    
DOI: 10.1007/s00205-012-0529-0     Document Type: Article
Times cited : (54)

References (46)
  • 1
    • 70350654241 scopus 로고    scopus 로고
    • The Cauchy problem and the martingale problem for integro-differential operators with non-smooth kernels
    • Abels H., Kassmann M.: The Cauchy problem and the martingale problem for integro-differential operators with non-smooth kernels. Osaka J. Math. 46(3), 661-683 (2009).
    • (2009) Osaka J. Math. , vol.46 , Issue.3 , pp. 661-683
    • Abels, H.1    Kassmann, M.2
  • 2
    • 84949351553 scopus 로고
    • Équations d'Hamilton-Jacobi du premier ordre avec termes intégro-différentiels. I. Unicité des solutions de viscosité
    • Awatif S.: Équations d'Hamilton-Jacobi du premier ordre avec termes intégro-différentiels. I. Unicité des solutions de viscosité. Commum. Partial Differ. Equ. 16(6-7), 1057-1074 (1991).
    • (1991) Commum. Partial Differ. Equ. , vol.16 , Issue.6-7 , pp. 1057-1074
    • Awatif, S.1
  • 3
    • 42549114402 scopus 로고    scopus 로고
    • On the dirichlet problem for second-order elliptic integro-differential equations
    • 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) Indiana Univ. Math. J. , vol.57 , Issue.1 , pp. 213-246
    • Barles, G.1    Chasseigne, E.2    Imbert, C.3
  • 4
    • 78650409141 scopus 로고    scopus 로고
    • Hölder continuity of solutions of second-order elliptic integro-differential equations
    • Barles G., Chasseigne E., Imbert C.: Hölder continuity of solutions of second-order elliptic integro-differential equations. J. Eur. Math. Soc. 13(1), 1-26 (2011).
    • (2011) J. Eur. Math. Soc. , vol.13 , Issue.1 , pp. 1-26
    • Barles, G.1    Chasseigne, E.2    Imbert, C.3
  • 5
    • 43049183444 scopus 로고    scopus 로고
    • Second-order elliptic integro-differential equations: viscosity solutions' theory revisited
    • Barles G., Imbert C.: Second-order elliptic integro-differential equations: viscosity solutions' theory revisited. Ann. Inst. H. Poincaré Anal. Non Linéaire 25(3), 567-585 (2008).
    • (2008) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.25 , Issue.3 , pp. 567-585
    • Barles, G.1    Imbert, C.2
  • 6
    • 62549135472 scopus 로고    scopus 로고
    • Non-local Dirichlet forms and symmetric jump processes
    • Barlow M. T., Bass R. F., Chen Z.-Q., Kassmann M.: Non-local Dirichlet forms and symmetric jump processes. Trans. Am. Math. Soc. 361(4), 1963-1999 (2009).
    • (2009) Trans. Am. Math. Soc. , vol.361 , Issue.4 , pp. 1963-1999
    • Barlow, M.T.1    Bass, R.F.2    Chen, Z.-Q.3    Kassmann, M.4
  • 7
    • 13844296740 scopus 로고    scopus 로고
    • Harnack inequalities for non-local operators of variable order
    • (electronic)
    • Bass, R. F., Kassmann, M.: Harnack inequalities for non-local operators of variable order. Trans. Am. Math. Soc. 357(2), 837-850 (electronic) (2005).
    • (2005) Trans. Am. Math. Soc. , vol.357 , Issue.2 , pp. 837-850
    • Bass, R.F.1    Kassmann, M.2
  • 8
    • 27744559009 scopus 로고    scopus 로고
    • Hölder continuity of harmonic functions with respect to operators of variable order. Commun
    • Bass R. F., Kassmann M.: Hölder continuity of harmonic functions with respect to operators of variable order. Commun. Partial Differ. Equ. 30(7-9), 1249-1259 (2005).
    • (2005) Partial Differ. Equ. , vol.30 , Issue.7-9 , pp. 1249-1259
    • Bass, R.F.1    Kassmann, M.2
  • 9
    • 0141457561 scopus 로고    scopus 로고
    • Harnack inequalities for jump processes
    • Bass R. F., Levin D. A.: Harnack inequalities for jump processes. Potential Anal. 17(4), 375-388 (2002).
    • (2002) Potential Anal. , vol.17 , Issue.4 , pp. 375-388
    • Bass, R.F.1    Levin, D.A.2
  • 10
    • 0035998083 scopus 로고    scopus 로고
    • Transition probabilities for symmetric jump processes
    • (electronic)
    • Bass, R. F., Levin, D. A.: Transition probabilities for symmetric jump processes. Trans. Am. Math. Soc. 354(7), 2933-2953 (electronic) (2002).
    • (2002) Trans. Am. Math. Soc. , vol.354 , Issue.7 , pp. 2933-2953
    • Bass, R.F.1    Levin, D.A.2
  • 11
  • 12
    • 0016038240 scopus 로고
    • The smoothness of solutions to nonlinear variational inequalities
    • Brézis H., Kinderlehrer D.: The smoothness of solutions to nonlinear variational inequalities. Indiana Univ. Math. J. 23, 831-844 (1973/1974).
    • (1973) Indiana Univ. Math. J. , vol.23 , pp. 831-844
    • Brézis, H.1    Kinderlehrer, D.2
  • 13
    • 0040059911 scopus 로고    scopus 로고
    • On viscosity solutions of fully nonlinear equations with measurable ingredients
    • Caffarelli L., Crandall M. G., Kocan M., Swi{ogonek}ch A.: On viscosity solutions of fully nonlinear equations with measurable ingredients. Commun. Pure Appl. Math. 49(4), 365-397 (1996).
    • (1996) Commun. Pure Appl. Math. , vol.49 , Issue.4 , pp. 365-397
    • Caffarelli, L.1    Crandall, M.G.2    Kocan, M.3    Swich, A.4
  • 16
    • 80051771417 scopus 로고    scopus 로고
    • The Evans-Krylov theorem for non local fully non linear equations
    • (to appear)
    • Caffarelli, L. A., Silvestre, L.: The Evans-Krylov theorem for non local fully non linear equations. Ann. Math. (2) (2012) (to appear).
    • (2012) Ann. Math. , vol.2
    • Caffarelli, L.A.1    Silvestre, L.2
  • 17
    • 79952706153 scopus 로고    scopus 로고
    • Regularity results for nonlocal equations by approximation
    • (to appear)
    • Caffarelli, L. A., Silvestre, L.: Regularity results for nonlocal equations by approximation. Arch. Rational. Mech. Anal. (2012) (to appear).
    • (2012) Arch. Rational. Mech. Anal.
    • Caffarelli, L.A.1    Silvestre, L.2
  • 18
    • 68049121967 scopus 로고    scopus 로고
    • Regularity theory for fully nonlinear integro-differential equations
    • Caffarelli L., Silvestre L.: Regularity theory for fully nonlinear 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
  • 20
    • 0000898166 scopus 로고
    • Interior a priori estimates for solutions of fully nonlinear equations
    • Caffarelli, L. A.: Interior a priori estimates for solutions of fully nonlinear equations. Ann. Math. (2) 130(1), 189-213 (1989).
    • (1989) Ann. Math. (2) , vol.130 , Issue.1 , pp. 189-213
    • Caffarelli, L.A.1
  • 21
    • 84881031051 scopus 로고
    • American Mathematical Society Colloquium Publications. American Mathematical Society, Providence
    • Caffarelli, L. A., Cabré, X.: Fully Nonlinear Elliptic Equations Vol. 43 of American Mathematical Society Colloquium Publications. American Mathematical Society, Providence, 1995.
    • (1995) Fully Nonlinear Elliptic Equations , vol.43
    • Caffarelli, L.A.1    Cabré, X.2
  • 22
    • 13844316338 scopus 로고    scopus 로고
    • Homogenization of fully nonlinear, uniformly elliptic and parabolic partial differential equations in stationary ergodic media. Commun
    • Caffarelli L. A., Souganidis P. E., Wang L.: Homogenization of fully nonlinear, uniformly elliptic and parabolic partial differential equations in stationary ergodic media. Commun. Pure Appl. Math. 58(3), 319-361 (2005).
    • (2005) Pure Appl. Math. , vol.58 , Issue.3 , pp. 319-361
    • Caffarelli, L.A.1    Souganidis, P.E.2    Wang, L.3
  • 23
    • 1342318409 scopus 로고    scopus 로고
    • Chapman & Hall/CRC Financial Mathematics Series. Chapman & Hall/CRC, Boca Raton
    • Cont, R., Tankov, P.: Financial Modelling with Jump Processes. Chapman & Hall/CRC Financial Mathematics Series. Chapman & Hall/CRC, Boca Raton, 2004.
    • (2004) Financial Modelling with Jump Processes
    • Cont, R.1    Tankov, P.2
  • 24
    • 21244498895 scopus 로고    scopus 로고
    • Integro-differential equations for option prices in exponential Lévy models
    • Cont R., Voltchkova E.: Integro-differential equations for option prices in exponential Lévy models. Finance Stoch. 9(3), 299-325 (2005).
    • (2005) Finance Stoch. , vol.9 , Issue.3 , pp. 299-325
    • Cont, R.1    Voltchkova, E.2
  • 25
    • 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
  • 26
    • 0000078158 scopus 로고
    • An inequality for hyperbolic polynomials
    • Garding L.: An inequality for hyperbolic polynomials. J. Math. Mech. 8, 957-965 (1959).
    • (1959) J. Math. Mech. , vol.8 , pp. 957-965
    • Garding, L.1
  • 27
    • 0031116136 scopus 로고    scopus 로고
    • Phase segregation dynamics in particle systems with long range interactions. I. Macroscopic limits
    • Giacomin G., Lebowitz J. L.: Phase segregation dynamics in particle systems with long range interactions. I. Macroscopic limits. J. Stat. Phys. 87(1-2), 37-61 (1997).
    • (1997) J. Stat. Phys. , vol.87 , Issue.1-2 , pp. 37-61
    • Giacomin, G.1    Lebowitz, J.L.2
  • 29
    • 57049132103 scopus 로고    scopus 로고
    • Nonlocal operators with applications to image processing
    • Gilboa G., Osher S.: Nonlocal operators with applications to image processing. Multiscale Model. Simul. 7(3), 1005-1028 (2008).
    • (2008) Multiscale Model. Simul. , vol.7 , Issue.3 , pp. 1005-1028
    • Gilboa, G.1    Osher, S.2
  • 30
    • 84966259849 scopus 로고
    • A uniqueness result for viscosity solutions of second order fully nonlinear partial differential equations
    • Jensen R., Lions P.-L., Souganidis P. E.: A uniqueness result for viscosity solutions of second order fully nonlinear partial differential equations. Proc. Am. Math. Soc. 102(4), 975-978 (1988).
    • (1988) Proc. Am. Math. Soc. , vol.102 , Issue.4 , pp. 975-978
    • Jensen, R.1    Lions, P.-L.2    Souganidis, P.E.3
  • 31
    • 84866371999 scopus 로고    scopus 로고
    • personal communication
    • Kassmann, M.: personal communication (2010).
    • (2010)
    • Kassmann, M.1
  • 34
    • 0003643984 scopus 로고
    • Springer, New York, (Translated from the Russian by A. P. Doohovskoy, Die Grundlehren der mathematischen Wissenschaften, Band 180)
    • Landkof, N. S.: Foundations of Modern Potential Theory. Springer, New York, 1972 (Translated from the Russian by A. P. Doohovskoy, Die Grundlehren der mathematischen Wissenschaften, Band 180).
    • (1972) Foundations of Modern Potential Theory
    • Landkof, N.S.1
  • 35
    • 51249173208 scopus 로고
    • A remark on regularization in Hilbert spaces
    • Lasry J.-M., Lions P.-L.: A remark on regularization in Hilbert spaces. Israel J. Math. 55(3), 257-266 (1986).
    • (1986) Israel J. Math. , vol.55 , Issue.3 , pp. 257-266
    • Lasry, J.-M.1    Lions, P.-L.2
  • 36
    • 34250457343 scopus 로고
    • On existence and smoothness of solutions of some non-coercive variational inequalities. Arch
    • Lewy H., Stampacchia G.: On existence and smoothness of solutions of some non-coercive variational inequalities. Arch. Rational Mech. Anal. 41, 241-253 (1971).
    • (1971) Rational Mech. Anal. , vol.41 , pp. 241-253
    • Lewy, H.1    Stampacchia, G.2
  • 37
    • 84968521780 scopus 로고
    • p-estimates for elliptic equations of nondivergent type
    • p-estimates for elliptic equations of nondivergent type. Proc. Am. Math. Soc. 96(3), 447-451 (1986).
    • (1986) Proc. Am. Math. Soc. , vol.96 , Issue.3 , pp. 447-451
    • Lin, F.-H.1
  • 38
    • 44349176723 scopus 로고    scopus 로고
    • The convex envelope is the solution of a nonlinear obstacle problem
    • (electronic)
    • Oberman A. M.: The convex envelope is the solution of a nonlinear obstacle problem. Proc. Am. Math. Soc. 135(6), 1689-1694 (electronic)(2007).
    • (2007) Proc. Am. Math. Soc. , vol.135 , Issue.6 , pp. 1689-1694
    • Oberman, A.M.1
  • 39
    • 0031677847 scopus 로고    scopus 로고
    • Optimal stopping of controlled jump diffusion processes: a viscosity solution approach
    • (electronic)
    • Pham H.: Optimal stopping of controlled jump diffusion processes: a viscosity solution approach. J. Math. Syst. Estim. Control8(1), 27 (electronic) (1998).
    • (1998) J. Math. Syst. Estim. Control , vol.8 , Issue.1 , pp. 27
    • Pham, H.1
  • 40
    • 79251483808 scopus 로고    scopus 로고
    • Periodic homogenization for nonlinear integro-differential equations
    • Schwab R. W.: Periodic homogenization for nonlinear integro-differential equations. SIAM J. Math. Anal. 42(6), 2652-2680 (2010).
    • (2010) SIAM J. Math. Anal. , vol.42 , Issue.6 , pp. 2652-2680
    • Schwab, R.W.1
  • 42
    • 33747032243 scopus 로고    scopus 로고
    • Hölder estimates for solutions of integro-differential equations like the fractional Laplace. Indiana Univ
    • Silvestre L.: Hölder estimates for solutions of integro-differential equations like the fractional Laplace. Indiana Univ. Math. J. 55(3), 1155-1174 (2006).
    • (2006) Math. J. , vol.55 , Issue.3 , pp. 1155-1174
    • Silvestre, L.1
  • 43
    • 33751514593 scopus 로고    scopus 로고
    • Regularity of the obstacle problem for a fractional power of the Laplace operator
    • Silvestre L.: Regularity of the obstacle problem for a fractional power of the Laplace operator. Commun. Pure Appl. Math. 60(1), 67-112 (2007).
    • (2007) Commun. Pure Appl. Math. , vol.60 , Issue.1 , pp. 67-112
    • Silvestre, L.1
  • 44
    • 0022806544 scopus 로고
    • Optimal control with state-space constraint. II. SIAM J
    • Soner H. M.: Optimal control with state-space constraint. II. SIAM J. Control Optim. 24(6), 1110-1122 (1986).
    • (1986) Control Optim. , vol.24 , Issue.6 , pp. 1110-1122
    • Soner, H.M.1
  • 45
    • 11544313334 scopus 로고
    • Optimal control of jump-Markov processes and viscosity solutions
    • Stochastic differential systems, stochastic control theory and applications (Minneapolis, MN, 1986), IMA Springer, New York
    • Soner, H. M.: Optimal control of jump-Markov processes and viscosity solutions. In: Stochastic differential systems, stochastic control theory and applications (Minneapolis, MN, 1986), Vol. 10 IMA Vol. Math. Appl., pp. 501-511. Springer, New York, 1988.
    • (1988) Math. Appl. , vol.10 , pp. 501-511
    • Soner, H.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.