메뉴 건너뛰기




Volumn 180, Issue 2, 2010, Pages 301-360

Rates of convergence for the homogenization of fully nonlinear uniformly elliptic pde in random media

Author keywords

[No Author keywords available]

Indexed keywords


EID: 77951203628     PISSN: 00209910     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00222-009-0230-6     Document Type: Article
Times cited : (86)

References (31)
  • 2
    • 0013004475 scopus 로고    scopus 로고
    • A note on nonlinear homogenization
    • Caffarelli, L. A.: A note on nonlinear homogenization. Commun. Pure Appl. Math. 52(7), 829-838 (1999).
    • (1999) Commun. Pure Appl. Math. , vol.52 , Issue.7 , pp. 829-838
    • Caffarelli, L.A.1
  • 3
    • 51249181477 scopus 로고
    • Potential methods in variational inequalities
    • Caffarelli, L. A., Kinderlehrer, D.: Potential methods in variational inequalities. J. Anal. Math. 37, 285-295 (1980).
    • (1980) J. Anal. Math. , vol.37 , pp. 285-295
    • Caffarelli, L.A.1    Kinderlehrer, D.2
  • 4
    • 37649004216 scopus 로고    scopus 로고
    • A rate of convergence for monotone finite difference approximations to fully nonlinear uniformly elliptic pde
    • Caffarelli, L. A., Souganidis, P. E.: A rate of convergence for monotone finite difference approximations to fully nonlinear uniformly elliptic pde. Commun. Pure Appl. Math. 61(1), 1-17 (2008).
    • (2008) Commun. Pure Appl. Math. , vol.61 , Issue.1 , pp. 1-17
    • Caffarelli, L.A.1    Souganidis, P.E.2
  • 5
    • 85056018509 scopus 로고    scopus 로고
    • Stochastic homogenization of fully nonlinear, uniformly elliptic and parabolic partial differential equations in stationary ergodic media
    • Caffarelli, L. A., Souganidis, P. E., Wang, L.: Stochastic homogenization of fully nonlinear, uniformly elliptic and parabolic partial differential equations in stationary ergodic media. Commun. Pure Appl. Math. 30(1-3), 335-375 (2005).
    • (2005) Commun. Pure Appl. Math. , vol.30 , Issue.1-3 , pp. 335-375
    • Caffarelli, L.A.1    Souganidis, P.E.2    Wang, L.3
  • 6
    • 67650727363 scopus 로고    scopus 로고
    • Rates of convergence in periodic homogenization of fully nonlinear uniformly elliptic PDEs
    • Camilli, F., Marchi, C.: Rates of convergence in periodic homogenization of fully nonlinear uniformly elliptic PDEs. Nonlinearity 22, 1481-1498 (2009).
    • (2009) Nonlinearity , vol.22 , pp. 1481-1498
    • Camilli, F.1    Marchi, C.2
  • 7
    • 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. AMS 27, 1-67 (1992).
    • (1992) Bull. AMS , vol.27 , pp. 1-67
    • Crandall, M.G.1    Ishii, H.2    Lions, P.-L.3
  • 8
    • 0002521237 scopus 로고
    • Nonlinear stochastic homogenization and ergodic theory
    • Dal Maso, G., Modica, L.: Nonlinear stochastic homogenization and ergodic theory. J. Reine Angew. Math. 368, 28-42 (1986).
    • (1986) J. Reine Angew. Math. , vol.368 , pp. 28-42
    • Dal Maso, G.1    Modica, L.2
  • 9
    • 84971110219 scopus 로고
    • The perturbed test function method for viscosity solutions of nonlinear PDE
    • Evans, L. C.: The perturbed test function method for viscosity solutions of nonlinear PDE. Proc. R. Soc. Edinb. Sect. A 111(3-4), 359-375 (1989).
    • (1989) Proc. R. Soc. Edinb. Sect. A , vol.111 , Issue.3-4 , pp. 359-375
    • Evans, L.C.1
  • 10
    • 84974059058 scopus 로고
    • Periodic homogenisation of certain fully nonlinear partial differential equations
    • Evans, L. C.: Periodic homogenisation of certain fully nonlinear partial differential equations. Proc. R. Soc. Edinburgh Sect. A 120(3-4), 245-265 (1992).
    • (1992) Proc. R. Soc. Edinburgh Sect. A , vol.120 , Issue.3-4 , pp. 245-265
    • Evans, L.C.1
  • 11
    • 0035589103 scopus 로고    scopus 로고
    • Effective Hamiltonians and averaging for Hamiltonian dynamics. I
    • Evans, L. C., Gomes, D.: Effective Hamiltonians and averaging for Hamiltonian dynamics. I. Arch. Ration. Mech. Anal. 157(1), 1-33 (2001).
    • (2001) Arch. Ration. Mech. Anal. , vol.157 , Issue.1 , pp. 1-33
    • Evans, L.C.1    Gomes, D.2
  • 12
    • 84968500878 scopus 로고
    • p-integrability of Green's functions and fundamental solutions for elliptic and parabolic equations
    • p-integrability of Green's functions and fundamental solutions for elliptic and parabolic equations. Duke Math. J. 51(4), 997-1016 (1984).
    • (1984) Duke Math. J. , vol.51 , Issue.4 , pp. 997-1016
    • Fabes, E.B.1    Stroock, D.2
  • 13
    • 63549106706 scopus 로고    scopus 로고
    • A stochastic representation for fully nonlinear pdes and its application to homogenization
    • Ichihara, N.: A stochastic representation for fully nonlinear pdes and its application to homogenization. J. Math. Sci. Univ. Tokyo 12, 467-492 (2005).
    • (2005) J. Math. Sci. Univ. Tokyo , vol.12 , pp. 467-492
    • Ichihara, N.1
  • 14
    • 3042693069 scopus 로고    scopus 로고
    • Almost periodic homogenization of Hamilton-Jacobi equations
    • Berlin1999, River Edge: World Sci. Publ
    • Ishii, H.: Almost periodic homogenization of Hamilton-Jacobi equations. In: International Conference on Differential Equations, vols. 1, 2, Berlin, 1999, pp. 600-605. World Sci. Publ., River Edge (2000).
    • (2000) International Conference on Differential Equations , vol.1-2 , pp. 600-605
    • Ishii, H.1
  • 15
    • 84966259849 scopus 로고
    • A uniqueness result for viscosity solutions of fully nonlinear second order partial differential equations
    • Jensen, R., Lions, P.-L., Souganidis, P. E.: A uniqueness result for viscosity solutions of fully nonlinear second order partial differential equations. Proc. Am. Math. Soc. 4, 975-978 (1988).
    • (1988) Proc. Am. Math. Soc. , vol.4 , pp. 975-978
    • Jensen, R.1    Lions, P.-L.2    Souganidis, P.E.3
  • 17
    • 52349108062 scopus 로고    scopus 로고
    • Homogenization of Hamilton-Jacobi-Bellman equations with respect to time-space shifts in a stationary ergodic medium
    • Kosygina, E., Varadhan, S. R. S.: Homogenization of Hamilton-Jacobi-Bellman equations with respect to time-space shifts in a stationary ergodic medium. Commun. Pure Appl. Math. 61(6), 816-847 (2007).
    • (2007) Commun. Pure Appl. Math. , vol.61 , Issue.6 , pp. 816-847
    • Kosygina, E.1    Varadhan, S.R.S.2
  • 18
    • 33748290005 scopus 로고    scopus 로고
    • Stochastic homogenization of Hamilton-Jacobi-Bellman equations
    • Kosygina, E., Rezankhanlou, F., Varadhan, S. R. S.: Stochastic homogenization of Hamilton-Jacobi-Bellman equations. Commun. Pure Appl. Math. 59(10), 1489-1521 (2006).
    • (2006) Commun. Pure Appl. Math. , vol.59 , Issue.10 , pp. 1489-1521
    • Kosygina, E.1    Rezankhanlou, F.2    Varadhan, S.R.S.3
  • 19
    • 0002902088 scopus 로고
    • The method of averaging and walk in inhomogeneous environments
    • Kozlov, S. M.: The method of averaging and walk in inhomogeneous environments. Russ. Math. Surv. 40, 73-145 (1985).
    • (1985) Russ. Math. Surv. , vol.40 , pp. 73-145
    • Kozlov, S.M.1
  • 20
    • 0041357028 scopus 로고    scopus 로고
    • Correctors for the homogenization of Hamilton-Jacobi equations in a stationary ergodic setting
    • Lions, P.-L., Souganidis, P. E.: Correctors for the homogenization of Hamilton-Jacobi equations in a stationary ergodic setting. Commun. Pure Appl. Math. 56(10), 1501-1524 (2003).
    • (2003) Commun. Pure Appl. Math. , vol.56 , Issue.10 , pp. 1501-1524
    • Lions, P.-L.1    Souganidis, P.E.2
  • 21
    • 17444412675 scopus 로고    scopus 로고
    • Homogenization for "viscous" Hamilton-Jacobi equations in stationary, ergodic media
    • Lions, P.-L., Souganidis, P. E.: Homogenization for "viscous" Hamilton-Jacobi equations in stationary, ergodic media. Commun. Part. Differ. Equs. 30(1-3), 335-376 (2005).
    • (2005) Commun. Part. Differ. Equs. , vol.30 , Issue.1-3 , pp. 335-376
    • Lions, P.-L.1    Souganidis, P.E.2
  • 22
    • 24944549463 scopus 로고    scopus 로고
    • Homogenization of degenerate second-order pde in periodic and almost periodic environments and applications
    • Lions, P.-L., Souganidis, P. E.: Homogenization of degenerate second-order pde in periodic and almost periodic environments and applications. Ann. Inst. H. Poincare, Anal. Non Lineaire 22(5), 667-677 (2005).
    • (2005) Ann. Inst. H. Poincare, Anal. Non Lineaire , vol.22 , Issue.5 , pp. 667-677
    • Lions, P.-L.1    Souganidis, P.E.2
  • 24
    • 0002558785 scopus 로고
    • Large-scale front dynamics for turbulent reaction-diffusion equations with separated velocity scales
    • Majda, A., Souganidis, P. E.: Large-scale front dynamics for turbulent reaction-diffusion equations with separated velocity scales. Nonlinearity 7(1), 1-30 (1994).
    • (1994) Nonlinearity , vol.7 , Issue.1 , pp. 1-30
    • Majda, A.1    Souganidis, P.E.2
  • 27
    • 0040786278 scopus 로고    scopus 로고
    • Homogenization for stochastic Hamilton-Jacobi equations
    • Rezankhanlou, F., Tarver, J.: Homogenization for stochastic Hamilton-Jacobi equations. Arch. Ration. Mech. Anal. 151, 277-309 (2000).
    • (2000) Arch. Ration. Mech. Anal. , vol.151 , pp. 277-309
    • Rezankhanlou, F.1    Tarver, J.2
  • 28
    • 67449105856 scopus 로고    scopus 로고
    • Homogenization of Hamilton-Jacobi equations in space-time stationary ergodic medium
    • Schwab, R.: Homogenization of Hamilton-Jacobi equations in space-time stationary ergodic medium. Indiana Univ. Math. J. 58(2), 537-582 (2009).
    • (2009) Indiana Univ. Math. J. , vol.58 , Issue.2 , pp. 537-582
    • Schwab, R.1
  • 29
    • 0009937623 scopus 로고    scopus 로고
    • Stochastic homogenization for Hamilton-Jacobi equations and applications
    • Souganidis, P. E.: Stochastic homogenization for Hamilton-Jacobi equations and applications. Asymptot. Anal. 20, 1-11 (1999).
    • (1999) Asymptot. Anal. , vol.20 , pp. 1-11
    • Souganidis, P.E.1
  • 30
    • 77951208731 scopus 로고
    • On the homogenization of boundary value problems with random coefficients
    • English transl.: Sib. Math. J. 21, 470-482 (1981)
    • Yurinskii, V. V.: On the homogenization of boundary value problems with random coefficients. Sib. Mat. Zh. 21(3), 209-223 (1980). (English transl.: Sib. Math. J. 21, 470-482 (1981)).
    • (1980) Sib. Mat. Zh. , vol.21 , Issue.3 , pp. 209-223
    • Yurinskii, V.V.1
  • 31
    • 34250147696 scopus 로고
    • On the homogenization of non-divergent second order equations with random coefficients
    • English transl.: Sib. Mat. J. 23, 276-287 (1982)
    • Yurinskii, V. V.: On the homogenization of non-divergent second order equations with random coefficients. Sib. Mat. Zh. 23(2), 176-188 (1982). (English transl.: Sib. Mat. J. 23, 276-287 (1982)).
    • (1982) Sib. Mat. Zh. , vol.23 , Issue.2 , pp. 176-188
    • Yurinskii, V.V.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.