메뉴 건너뛰기




Volumn 61, Issue 1, 2008, Pages 1-17

A rate of convergence for monotone finite difference approximations to fully nonlinear, uniformly elliptic PDEs

Author keywords

[No Author keywords available]

Indexed keywords


EID: 37649004216     PISSN: 00103640     EISSN: 00103640     Source Type: Journal    
DOI: 10.1002/cpa.20208     Document Type: Article
Times cited : (73)

References (29)
  • 1
    • 0036012033 scopus 로고    scopus 로고
    • On the convergence rate of approximation schemes for Hamilton-Jacobi-Bellman equations
    • Barles, G.; Jakobsen, E. R. On the convergence rate of approximation schemes for Hamilton-Jacobi-Bellman equations. M2AN Math. Model. Numer. Anal. 36 (2002), no. 1, 33-54.
    • (2002) M2AN Math. Model. Numer. Anal , vol.36 , Issue.1 , pp. 33-54
    • Barles, G.1    Jakobsen, E.R.2
  • 2
    • 25444517488 scopus 로고    scopus 로고
    • Barles, G.; Jakobsen, E. R. Error bounds for monotone approximation schemes for Hamilton-Jacobi-Bellman equations. SIAM J. Numer. Anal. 43 (2005), no. 2, 540-558 (electronic). Available online at: http://www.math.ntnu.no/~erj/publications.html
    • Barles, G.; Jakobsen, E. R. Error bounds for monotone approximation schemes for Hamilton-Jacobi-Bellman equations. SIAM J. Numer. Anal. 43 (2005), no. 2, 540-558 (electronic). Available online at: http://www.math.ntnu.no/~erj/publications.html
  • 3
    • 84974753170 scopus 로고
    • Convergence of approximation schemes for fully nonlinear second order equations
    • Barles, G.; Souganidis, P. E. Convergence of approximation schemes for fully nonlinear second order equations. Asymptotic Anal. 4 (1991), no. 3, 271-283.
    • (1991) Asymptotic Anal , vol.4 , Issue.3 , pp. 271-283
    • Barles, G.1    Souganidis, P.E.2
  • 4
    • 30344455936 scopus 로고    scopus 로고
    • Error estimates for stochastic differential games: The adverse stopping case
    • Bonnans, J. F.; Maroso, S.; Zidani, H. Error estimates for stochastic differential games: the adverse stopping case. IMA J. Numer. Anal. 26 (2006), no. 1, 188-212.
    • (2006) IMA J. Numer. Anal , vol.26 , Issue.1 , pp. 188-212
    • Bonnans, J.F.1    Maroso, S.2    Zidani, H.3
  • 5
    • 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. of Math. (2) 130 (1989), no. 1, 189-213.
    • (1989) Ann. of Math. (2) , vol.130 , Issue.1 , pp. 189-213
    • Caffarelli, L.A.1
  • 7
    • 37649024959 scopus 로고    scopus 로고
    • Rate of convergence for stochastic homogenization of uniformly elliptic partial differential equations
    • Preprint
    • Caffarelli, L.; Souganidis, P. E. Rate of convergence for stochastic homogenization of uniformly elliptic partial differential equations. Preprint.
    • Caffarelli, L.1    Souganidis, P.E.2
  • 8
    • 37649014054 scopus 로고    scopus 로고
    • Caffarelli, L. A.; Wang, L. A Harnack inequality approach to the interior regularity of elliptic equations. Indiana Univ. Math. J. 42 (1993), no. 1, 145-157.
    • Caffarelli, L. A.; Wang, L. A Harnack inequality approach to the interior regularity of elliptic equations. Indiana Univ. Math. J. 42 (1993), no. 1, 145-157.
  • 9
    • 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. Amer. Math. Soc. (N.S.) 27 (1992), no. 1, 1-67.
    • (1992) Bull. Amer. Math. Soc. (N.S.) , vol.27 , Issue.1 , pp. 1-67
    • Crandall, M.G.1    Ishii, H.2    Lions, P.-L.3
  • 10
    • 84966245867 scopus 로고
    • Two approximations of solutions of Hamilton-Jacobi equations
    • Crandall, M. G.; Lions, P.-L. Two approximations of solutions of Hamilton-Jacobi equations. Math. Comp. 43 (1984), no. 167, 1-19.
    • (1984) Math. Comp , vol.43 , Issue.167 , pp. 1-19
    • Crandall, M.G.1    Lions, P.-L.2
  • 11
    • 84990553687 scopus 로고
    • Classical solutions of fully nonlinear, convex, second-order elliptic equations
    • Evans, L. C. Classical solutions of fully nonlinear, convex, second-order elliptic equations. Comm. Pure Appl. Math. 35 (1982), no. 3, 333-363.
    • (1982) Comm. Pure Appl. Math , vol.35 , Issue.3 , pp. 333-363
    • Evans, L.C.1
  • 12
    • 4444250078 scopus 로고    scopus 로고
    • On error bounds for approximation schemes for non-convex degenerate elliptic equations
    • Jakobsen, E. R. On error bounds for approximation schemes for non-convex degenerate elliptic equations. BIT 44 (2004), no. 2, 269-285.
    • (2004) BIT , vol.44 , Issue.2 , pp. 269-285
    • Jakobsen, E.R.1
  • 13
    • 33748920037 scopus 로고    scopus 로고
    • On error bounds for monotone approximation schemes for multi-dimensional Isaacs equations
    • Jakobsen, E. R. On error bounds for monotone approximation schemes for multi-dimensional Isaacs equations. Asymptot. Anal. 49 (2006), no. 3-4, 249-273.
    • (2006) Asymptot. Anal , vol.49 , Issue.3-4 , pp. 249-273
    • Jakobsen, E.R.1
  • 14
    • 33646945027 scopus 로고
    • The maximum principle for viscosity solutions of fully nonlinear second order partial differential equations
    • Jensen, R. The maximum principle for viscosity solutions of fully nonlinear second order partial differential equations. Arch. Rational Mech. Anal. 101 (1988), no. 1, 1-27.
    • (1988) Arch. Rational Mech. Anal , vol.101 , Issue.1 , pp. 1-27
    • Jensen, R.1
  • 15
    • 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. Amer. Math. Soc. 102 (1988), no. 4, 975-978.
    • (1988) Proc. Amer. Math. Soc , vol.102 , Issue.4 , pp. 975-978
    • Jensen, R.1    Lions, P.-L.2    Souganidis, P.E.3
  • 16
    • 0000396066 scopus 로고
    • Boundedly inhomogeneous elliptic and parabolic equations
    • Krylov, N. V. Boundedly inhomogeneous elliptic and parabolic equations. Izv. Akad. Nauk SSSR Ser. Mat. 46 (1982), no. 3, 487-523;
    • (1982) Izv. Akad. Nauk SSSR Ser. Mat , vol.46 , Issue.3 , pp. 487-523
    • Krylov, N.V.1
  • 17
    • 84878313116 scopus 로고
    • translation in Math
    • translation in Math. USSR Izv. 20 (1983), 459-492.
    • (1983) USSR Izv , vol.20 , pp. 459-492
  • 18
    • 0002296910 scopus 로고
    • Boundedly inhomogeneous elliptic and parabolic equations in a domain
    • Krylov, N. V. Boundedly inhomogeneous elliptic and parabolic equations in a domain. Izv. Akad. Nauk SSSR Ser. Mat. 47 (1983), no. 1, 75-108;
    • (1983) Izv. Akad. Nauk SSSR Ser. Mat , vol.47 , Issue.1 , pp. 75-108
    • Krylov, N.V.1
  • 19
    • 37649014805 scopus 로고
    • translation in Math
    • translation in Math. USSR Izv. 22 (1984), 67-97.
    • (1984) USSR Izv , vol.22 , pp. 67-97
  • 20
    • 0007455893 scopus 로고    scopus 로고
    • On the rate of convergence of finite-difference approximations for Bellman's equations
    • Krylov, N. V. On the rate of convergence of finite-difference approximations for Bellman's equations. Algebra i Analiz 9 (1997), no. 3, 245-256;
    • (1997) Algebra i Analiz , vol.9 , Issue.3 , pp. 245-256
    • Krylov, N.V.1
  • 21
    • 0009900309 scopus 로고    scopus 로고
    • translation in St
    • translation in St. Petersburg Math. J. 9 (1998), no. 3, 639-650.
    • (1998) Petersburg Math. J , vol.9 , Issue.3 , pp. 639-650
  • 22
    • 0034384390 scopus 로고    scopus 로고
    • On the rate of convergence of finite-difference approximations for Bellman's equations with variable coefficients
    • Krylov, N. V. On the rate of convergence of finite-difference approximations for Bellman's equations with variable coefficients. Probab. Theory Related Fields 117 (2000), no. 1, 1-16.
    • (2000) Probab. Theory Related Fields , vol.117 , Issue.1 , pp. 1-16
    • Krylov, N.V.1
  • 23
    • 29644447250 scopus 로고    scopus 로고
    • The rate of convergence of finite-difference approximations for Bellman equations with Lipschitz coefficients
    • Krylov, N. V. The rate of convergence of finite-difference approximations for Bellman equations with Lipschitz coefficients. Appl. Math. Optim. 52 (2005), no. 3, 365-399.
    • (2005) Appl. Math. Optim , vol.52 , Issue.3 , pp. 365-399
    • Krylov, N.V.1
  • 24
    • 0013024444 scopus 로고
    • Linear elliptic difference inequalities with random coefficients
    • Kuo, H. J.; Trudinger, N. S. Linear elliptic difference inequalities with random coefficients. Math. Comp. 55 (1990), no. 191, 37-53.
    • (1990) Math. Comp , vol.55 , Issue.191 , pp. 37-53
    • Kuo, H.J.1    Trudinger, N.S.2
  • 25
    • 0026821779 scopus 로고
    • Discrete methods for fully nonlinear elliptic equations
    • Kuo, H. J.; Trudinger, N. S. Discrete methods for fully nonlinear elliptic equations. SIAM J. Numer. Anal. 29 (1992), no. 1, 123-135.
    • (1992) SIAM J. Numer. Anal , vol.29 , Issue.1 , pp. 123-135
    • Kuo, H.J.1    Trudinger, N.S.2
  • 26
    • 0000483302 scopus 로고    scopus 로고
    • Positive difference operators on general meshes
    • Kuo, H. J.; Trudinger, N. S. Positive difference operators on general meshes. Duke Math. J. 83 (1996), no. 2, 415-433.
    • (1996) Duke Math. J , vol.83 , Issue.2 , pp. 415-433
    • Kuo, H.J.1    Trudinger, N.S.2
  • 27
    • 46549091075 scopus 로고
    • Approximation schemes for viscosity solutions of Hamilton-Jacobi equations
    • Souganidis, P. E. Approximation schemes for viscosity solutions of Hamilton-Jacobi equations. J. Differential Equations 59 (1985), no. 1, 1-43.
    • (1985) J. Differential Equations , vol.59 , Issue.1 , pp. 1-43
    • Souganidis, P.E.1
  • 28
    • 37649001519 scopus 로고    scopus 로고
    • Trudinger, N. S. On regularity and existence of viscosity solutions of nonlinear second order, elliptic equations. Partial differential equations and the calculus of variations, 2, 939-957. Progress in Nonlinear Differential Equations and Their Applications, 2. Birkhäuser, Boston, 1989.
    • Trudinger, N. S. On regularity and existence of viscosity solutions of nonlinear second order, elliptic equations. Partial differential equations and the calculus of variations, vol. 2, 939-957. Progress in Nonlinear Differential Equations and Their Applications, 2. Birkhäuser, Boston, 1989.
  • 29
    • 84990619178 scopus 로고
    • On the regularity theory of fully nonlinear parabolic equations. II
    • Wang, L. On the regularity theory of fully nonlinear parabolic equations. II. Comm. Pure Appl. Math. 45 (1992), no. 2, 141-178.
    • (1992) Comm. Pure Appl. Math , vol.45 , Issue.2 , pp. 141-178
    • Wang, L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.