메뉴 건너뛰기




Volumn 17, Issue 3, 1998, Pages 165-184

Stochastic homogenization of elliptic boundary-value problems with Lp-data

Author keywords

Boundary value problem; Elliptic equation; Random coefficients; Randomly perforated domain; Stochastic homogenization

Indexed keywords


EID: 0000219488     PISSN: 09217134     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (38)

References (39)
  • 1
    • 21144473666 scopus 로고
    • Homogenization and two-scale convergence
    • G. Allaire, Homogenization and two-scale convergence, SIAM J. Math. Anal. 23 (1992), 1482-1518.
    • (1992) SIAM J. Math. Anal. , vol.23 , pp. 1482-1518
    • Allaire, G.1
  • 2
    • 84990602687 scopus 로고
    • Compactness methods in the theory of homogenization
    • M. Avallaneda and F.-H. Lin, Compactness methods in the theory of homogenization, Comm. Pure Appl. Math. 40 (1987), 803-847.
    • (1987) Comm. Pure Appl. Math. , vol.40 , pp. 803-847
    • Avallaneda, M.1    Lin, F.-H.2
  • 4
    • 84990613896 scopus 로고
    • Homogenization of elliptic problems with principal part not in divergence form and Hamiltonian with quadratic growth
    • A. Bensoussan, L. Boccardo and F. Murat, Homogenization of elliptic problems with principal part not in divergence form and Hamiltonian with quadratic growth, Comm. Pure Appl. Math. 39 (1986), 769-805.
    • (1986) Comm. Pure Appl. Math. , vol.39 , pp. 769-805
    • Bensoussan, A.1    Boccardo, L.2    Murat, F.3
  • 6
    • 84942225190 scopus 로고
    • Stochastic two-scale convergence in the mean and applications
    • A. Bourgeat, A. Mikelić and S. Wright, Stochastic two-scale convergence in the mean and applications, J. Reine Angew. Math. 56 (1994), 19-51.
    • (1994) J. Reine Angew. Math. , vol.56 , pp. 19-51
    • Bourgeat, A.1    Mikelić, A.2    Wright, S.3
  • 8
    • 0000941796 scopus 로고
    • q-estimates for Green's potentials on Lipschitz domains
    • q-estimates for Green's potentials on Lipschitz domains, Math. Scand. 44 (1979), 149-170.
    • (1979) Math. Scand. , vol.44 , pp. 149-170
    • Dahlberg, B.1
  • 10
    • 84972551990 scopus 로고
    • Boundary-value problems for the system of elastostatics in Lipschitz domains
    • B. Dahlberg, C. Kenig and G. Verchota, Boundary-value problems for the system of elastostatics in Lipschitz domains, Duke Math. J. 57 (1988), 795-818.
    • (1988) Duke Math. J. , vol.57 , pp. 795-818
    • Dahlberg, B.1    Kenig, C.2    Verchota, G.3
  • 11
    • 0000847583 scopus 로고
    • Nonlinear stochastic homogenization
    • G. Dal Maso and L. Modica, Nonlinear stochastic homogenization, Ann. Mat. Pura Appl. 144 (1986), 347-389.
    • (1986) Ann. Mat. Pura Appl. , vol.144 , pp. 347-389
    • Dal Maso, G.1    Modica, L.2
  • 12
    • 0000618557 scopus 로고
    • Sulla convergenza delli integrali dell energia per operatori ellittici del seconde ordine
    • E. De Giorgi and S. Spagnolo, Sulla convergenza delli integrali dell energia per operatori ellittici del seconde ordine, Boll. Un. Mat. Ital. 8 (1973), 391-411.
    • (1973) Boll. Un. Mat. Ital. , vol.8 , pp. 391-411
    • De Giorgi, E.1    Spagnolo, S.2
  • 14
    • 84865687708 scopus 로고
    • Boundary-value problems for the Stokes system in Lipschitz domains
    • E. Fabes, C. Kenig and G. Verchota, Boundary-value problems for the Stokes system in Lipschitz domains, Duke Math. J. 57 (1988), 769-793.
    • (1988) Duke Math. J. , vol.57 , pp. 769-793
    • Fabes, E.1    Kenig, C.2    Verchota, G.3
  • 15
    • 0002780973 scopus 로고
    • The theory of weights and the Dirichlet problem for elliptic equations
    • R. Fefferman, C. Kenig and J. Pipher, The theory of weights and the Dirichlet problem for elliptic equations, Ann. Math. 134 (1991), 65-124.
    • (1991) Ann. Math. , vol.134 , pp. 65-124
    • Fefferman, R.1    Kenig, C.2    Pipher, J.3
  • 17
    • 79953907620 scopus 로고
    • Averaging of functionals of the calculus of variations and elasticity theory
    • V.V. Jikov (V.V. Zhikov), Averaging of functionals of the calculus of variations and elasticity theory, Math. USSR-Izv. 29 (1987), 33-66.
    • (1987) Math. USSR-Izv. , vol.29 , pp. 33-66
    • Jikov, V.V.1
  • 18
    • 0345840512 scopus 로고
    • Problems of function extensions related to the theory ofhomogenization
    • V.V. Jikov, Problems of function extensions related to the theory ofhomogenization, Differential Equations 26 (1990), 33-14.
    • (1990) Differential Equations , vol.26 , pp. 33-114
    • Jikov, V.V.1
  • 19
    • 0346471392 scopus 로고
    • Asymptotic problems connected with the heat equation in perforated domains
    • V.V. Jikov, Asymptotic problems connected with the heat equation in perforated domains, Math. USSR-Sb. 71 (1992), 125-147.
    • (1992) Math. USSR-Sb. , vol.71 , pp. 125-147
    • Jikov, V.V.1
  • 21
    • 0345840513 scopus 로고
    • Averaging of a system in the theory of elasticity with almost-periodic coefficients
    • V.V. Jikov and O.A. Oleinik, Averaging of a system in the theory of elasticity with almost-periodic coefficients, Moscow Univ. Math. Bull. 37(6) (1982), 74-82.
    • (1982) Moscow Univ. Math. Bull. , vol.37 , Issue.6 , pp. 74-82
    • Jikov, V.V.1    Oleinik, O.A.2
  • 22
    • 0000324134 scopus 로고
    • Elliptic boundary-value problems on Lipschitz domains
    • C. Kenig, Elliptic boundary-value problems on Lipschitz domains, Ann. of Math. Stud. 112 (1986), 131-183.
    • (1986) Ann. of Math. Stud. , vol.112 , pp. 131-183
    • Kenig, C.1
  • 23
    • 0003307061 scopus 로고
    • Harmonic Analysis Techniques for Second-Order Elliptic Boundary-Value Problems
    • American Mathematical Society, Providence, RI
    • C. Kenig, Harmonic Analysis Techniques for Second-Order Elliptic Boundary-Value Problems, CBMS Regional Conf. Ser., Vol. 83, American Mathematical Society, Providence, RI, 1994.
    • (1994) CBMS Regional Conf. Ser. , vol.83
    • Kenig, C.1
  • 24
    • 0001403911 scopus 로고
    • The Neumann problem for elliptic equations with non-smooth coefficients
    • C. Kenig and J. Pipher, The Neumann problem for elliptic equations with non-smooth coefficients, Invent. Math. 113 (1993).
    • (1993) Invent. Math. , vol.113
    • Kenig, C.1    Pipher, J.2
  • 26
    • 0012460954 scopus 로고
    • Averaging random structures
    • S.M. Kozlov, Averaging random structures, Soviet Math. Dokl. 19 (1978), 950-954.
    • (1978) Soviet Math. Dokl. , vol.19 , pp. 950-954
    • Kozlov, S.M.1
  • 27
    • 0000254912 scopus 로고
    • Averaging of random operators
    • S.M. Kozlov, Averaging of random operators, Math. USSR-Sb. 37 (1980), 167-180.
    • (1980) Math. USSR-Sb. , vol.37 , pp. 167-180
    • Kozlov, S.M.1
  • 28
    • 0002902088 scopus 로고
    • The method of averaging and random walks in inhomogeneous environments
    • S.M. Kozlov, The method of averaging and random walks in inhomogeneous environments, Russian Math. Surveys 40 (1985), 73-145.
    • (1985) Russian Math. Surveys , vol.40 , pp. 73-145
    • Kozlov, S.M.1
  • 29
    • 0343600674 scopus 로고
    • The asymptotic behavior of solutions of the second boundary value problem under fragmentation of the boundary of the domain
    • E. Kruslov, The asymptotic behavior of solutions of the second boundary value problem under fragmentation of the boundary of the domain. Math. USSR-Sb. 35 (1979), 266-282.
    • (1979) Math. USSR-Sb. , vol.35 , pp. 266-282
    • Kruslov, E.1
  • 31
    • 0001253780 scopus 로고
    • p-estimate for the gradient of solutions of second-order elliptic divergence equations
    • p-estimate for the gradient of solutions of second-order elliptic divergence equations, Ann. Sci. Norm. Sup. Pisa 17 (1963), 189-206.
    • (1963) Ann. Sci. Norm. Sup. Pisa , vol.17 , pp. 189-206
    • Meyers, N.G.1
  • 32
    • 0000315621 scopus 로고
    • A general convergence result for a functional related to the theory of homogenization
    • G. Nguetseng, A general convergence result for a functional related to the theory of homogenization, SIAM J. Math. Anal. 20 (1989), 608-623.
    • (1989) SIAM J. Math. Anal. , vol.20 , pp. 608-623
    • Nguetseng, G.1
  • 33
    • 0000374920 scopus 로고
    • Homogenization of a diffusion process in a divergence-free random field
    • K. Oelschlager, Homogenization of a diffusion process in a divergence-free random field, Ann. Probab. 16(3) (1988), 1084-1126.
    • (1988) Ann. Probab. , vol.16 , Issue.3 , pp. 1084-1126
    • Oelschlager, K.1
  • 35
    • 0001689286 scopus 로고
    • Boundary value problems with rapidly oscillating random coefficients
    • J. Fritz, J.L. Lebowitz and D. Szasz, eds, North-Holland Amsterdam
    • G.C. Papanicolaou and S.R.S. Varadhan, Boundary value problems with rapidly oscillating random coefficients, in: Random Fields, J. Fritz, J.L. Lebowitz and D. Szasz, eds, North-Holland Amsterdam, 1981, pp. 835-873.
    • (1981) Random Fields , pp. 835-873
    • Papanicolaou, G.C.1    Varadhan, S.R.S.2
  • 36
    • 0345840510 scopus 로고
    • Higher integrability of the gradient in linear elasticity
    • P. Shi and S. Wright, Higher integrability of the gradient in linear elasticity, Math. Ann. 299 (1994), 435-448.
    • (1994) Math. Ann. , vol.299 , pp. 435-448
    • Shi, P.1    Wright, S.2
  • 38
    • 84923746772 scopus 로고    scopus 로고
    • Layer potentials and regularity for the Dirichlet problem for Laplace's equation
    • G. Verchota, Layer potentials and regularity for the Dirichlet problem for Laplace's equation, J. Funct. Anal. 59
    • J. Funct. Anal. , vol.59
    • Verchota, G.1
  • 39
    • 0347101743 scopus 로고
    • Homogenization of the Stokes equations with general random coefficients
    • S. Wright, Homogenization of the Stokes equations with general random coefficients, Z. Anal. Anwendungen 13 (1994), 405-416.
    • (1994) Z. Anal. Anwendungen , vol.13 , pp. 405-416
    • Wright, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.