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Volumn 250, Issue 1, 2007, Pages 167-196

Nonlinear elliptic equations with BMO coefficients in Reifenberg domains

Author keywords

BMO space; Maximal function; Nonlinear elliptic equations; Reifenberg domain; Vitali covering lemma; W1, q estimates

Indexed keywords


EID: 34547124558     PISSN: 00221236     EISSN: 10960783     Source Type: Journal    
DOI: 10.1016/j.jfa.2007.04.021     Document Type: Article
Times cited : (80)

References (31)
  • 1
    • 0000794929 scopus 로고    scopus 로고
    • Equivalence between regularity theorems and heat kernel estimates for higher order elliptic operators and systems under divergence form
    • Auscher P., and Qafsaoui M. Equivalence between regularity theorems and heat kernel estimates for higher order elliptic operators and systems under divergence form. J. Funct. Anal. 177 2 (2000) 310-364
    • (2000) J. Funct. Anal. , vol.177 , Issue.2 , pp. 310-364
    • Auscher, P.1    Qafsaoui, M.2
  • 2
    • 4544307605 scopus 로고    scopus 로고
    • Elliptic equations with BMO coefficients in Reifenberg domains
    • Byun S., and Wang L. Elliptic equations with BMO coefficients in Reifenberg domains. Comm. Pure Appl. Math. 57 10 (2004) 1283-1310
    • (2004) Comm. Pure Appl. Math. , vol.57 , Issue.10 , pp. 1283-1310
    • Byun, S.1    Wang, L.2
  • 3
    • 17844373003 scopus 로고    scopus 로고
    • p estimates for parabolic equations in Reifenberg domains
    • p estimates for parabolic equations in Reifenberg domains. J. Funct. Anal. 223 1 (2005) 44-85
    • (2005) J. Funct. Anal. , vol.223 , Issue.1 , pp. 44-85
    • Byun, S.1    Wang, L.2
  • 4
    • 0002449458 scopus 로고
    • Fully nonlinear elliptic equations
    • Amer. Math. Soc., Providence, RI
    • Caffarelli L.A., and Cabré X. Fully nonlinear elliptic equations. Amer. Math. Soc. Colloq. Publ. vol. 43 (1995), Amer. Math. Soc., Providence, RI
    • (1995) Amer. Math. Soc. Colloq. Publ. , vol.43
    • Caffarelli, L.A.1    Cabré, X.2
  • 5
    • 0041125729 scopus 로고    scopus 로고
    • 1, p estimates for elliptic equations in divergence form
    • 1, p estimates for elliptic equations in divergence form. Comm. Pure Appl. Math. 51 (1998) 1-21
    • (1998) Comm. Pure Appl. Math. , vol.51 , pp. 1-21
    • Caffarelli, L.A.1    Peral, I.2
  • 6
    • 1542782912 scopus 로고    scopus 로고
    • p estimates for divergence form elliptic equations with discontinuous coefficients
    • p estimates for divergence form elliptic equations with discontinuous coefficients. Boll. Unione Mat. Ital. Sez. A (7) 10 2 (1996) 409-420
    • (1996) Boll. Unione Mat. Ital. Sez. A (7) , vol.10 , Issue.2 , pp. 409-420
    • Di Fazio, G.1
  • 7
    • 0001016104 scopus 로고
    • Interior estimates in Morrey spaces for strong solutions to nondivergence form equations with discontinuous coefficients
    • Di Fazio G., and Ragusa M.A. Interior estimates in Morrey spaces for strong solutions to nondivergence form equations with discontinuous coefficients. J. Funct. Anal. 112 2 (1993) 241-256
    • (1993) J. Funct. Anal. , vol.112 , Issue.2 , pp. 241-256
    • Di Fazio, G.1    Ragusa, M.A.2
  • 8
    • 0038002274 scopus 로고    scopus 로고
    • Global Morrey regularity of strong solutions to the Dirichlet problem for elliptic equations with discontinuous coefficients
    • Di Fazio G., Palagachev D., and Ragusa M.A. Global Morrey regularity of strong solutions to the Dirichlet problem for elliptic equations with discontinuous coefficients. J. Funct. Anal. 166 2 (1999) 179-196
    • (1999) J. Funct. Anal. , vol.166 , Issue.2 , pp. 179-196
    • Di Fazio, G.1    Palagachev, D.2    Ragusa, M.A.3
  • 9
    • 0001472514 scopus 로고
    • 1 + α local regularity of weak solutions of degenerate elliptic equations
    • 1 + α local regularity of weak solutions of degenerate elliptic equations. Nonlinear Anal. 7 8 (1983) 827-850
    • (1983) Nonlinear Anal. , vol.7 , Issue.8 , pp. 827-850
    • DiBenedetto, E.1
  • 10
    • 0009396335 scopus 로고
    • On the higher integrability of the gradient of weak solutions of certain degenerate elliptic systems
    • DiBenedetto E., and Manfredi J. On the higher integrability of the gradient of weak solutions of certain degenerate elliptic systems. Amer. J. Math. 115 5 (1993) 1107-1134
    • (1993) Amer. J. Math. , vol.115 , Issue.5 , pp. 1107-1134
    • DiBenedetto, E.1    Manfredi, J.2
  • 11
    • 0030642447 scopus 로고    scopus 로고
    • Traces of Sobolev functions on fractal type sets and characterization of extension domains
    • Hajlasz P., and Martio O. Traces of Sobolev functions on fractal type sets and characterization of extension domains. J. Funct. Anal. 143 1 (1997) 221-246
    • (1997) J. Funct. Anal. , vol.143 , Issue.1 , pp. 221-246
    • Hajlasz, P.1    Martio, O.2
  • 12
    • 0011616405 scopus 로고
    • Potential Theory of Degenerate Elliptic Equations
    • Oxford Sci. Publ. Clarendon/Oxford Univ. Press, New York vi+363 pp
    • Heinonen J., Kilpelainen T., and Martio O. Potential Theory of Degenerate Elliptic Equations. Oxford Math. Monogr. (1993), Oxford Sci. Publ. Clarendon/Oxford Univ. Press, New York vi+363 pp
    • (1993) Oxford Math. Monogr.
    • Heinonen, J.1    Kilpelainen, T.2    Martio, O.3
  • 13
    • 0000417913 scopus 로고
    • p-estimates for degenerate elliptic operators
    • p-estimates for degenerate elliptic operators. Studia Math. 75 3 (1983) 293-312
    • (1983) Studia Math. , vol.75 , Issue.3 , pp. 293-312
    • Iwaniec, T.1
  • 14
    • 84980082306 scopus 로고
    • On functions of bounded mean oscillation
    • John F., and Nirenberg L. On functions of bounded mean oscillation. Comm. Pure Appl. Math. 14 (1961) 415-426
    • (1961) Comm. Pure Appl. Math. , vol.14 , pp. 415-426
    • John, F.1    Nirenberg, L.2
  • 15
    • 0002428795 scopus 로고
    • Quasiconformal mappings and extendability of functions in Sobolev spaces
    • Jones P.W. Quasiconformal mappings and extendability of functions in Sobolev spaces. Acta Math. 147 (1981) 71-88
    • (1981) Acta Math. , vol.147 , pp. 71-88
    • Jones, P.W.1
  • 16
    • 0033235413 scopus 로고    scopus 로고
    • Free boundary regularity for harmonic measures and the Poisson kernel
    • Kenig C., and Toro T. Free boundary regularity for harmonic measures and the Poisson kernel. Ann. of Math. (2) (1999) 367-454
    • (1999) Ann. of Math. (2) , pp. 367-454
    • Kenig, C.1    Toro, T.2
  • 17
    • 0037507524 scopus 로고    scopus 로고
    • Poisson kernel characterization of Reifenberg flat chord arc domains
    • Kenig C., and Toro T. Poisson kernel characterization of Reifenberg flat chord arc domains. Ann. Sci. École Norm. Sup. (4) 36 4 (2003) 323-401
    • (2003) Ann. Sci. École Norm. Sup. (4) , vol.36 , Issue.4 , pp. 323-401
    • Kenig, C.1    Toro, T.2
  • 18
    • 0033475519 scopus 로고    scopus 로고
    • A local estimate for nonlinear equations with discontinuous coefficients
    • Kinnunen J., and Zhou S. A local estimate for nonlinear equations with discontinuous coefficients. Comm. Partial Differential Equations 24 (1999) 2043-2068
    • (1999) Comm. Partial Differential Equations , vol.24 , pp. 2043-2068
    • Kinnunen, J.1    Zhou, S.2
  • 19
    • 33751098961 scopus 로고    scopus 로고
    • A boundary estimate for nonlinear equations with discontinuous coefficients
    • Kinnunen J., and Zhou S. A boundary estimate for nonlinear equations with discontinuous coefficients. Differential Integral Equations 14 (2001) 475-492
    • (2001) Differential Integral Equations , vol.14 , pp. 475-492
    • Kinnunen, J.1    Zhou, S.2
  • 20
    • 0001386460 scopus 로고
    • Regularity of the derivatives of solutions to certain degenerate elliptic equations
    • Lewis J. Regularity of the derivatives of solutions to certain degenerate elliptic equations. Indiana U. Math. J. 32 6 (1983) 849-858
    • (1983) Indiana U. Math. J. , vol.32 , Issue.6 , pp. 849-858
    • Lewis, J.1
  • 21
    • 0000405695 scopus 로고
    • Boundary regularity for solutions of degenerate elliptic equations
    • Lieberman G.M. Boundary regularity for solutions of degenerate elliptic equations. Nonlinear Anal. 12 11 (1988) 1203-1219
    • (1988) Nonlinear Anal. , vol.12 , Issue.11 , pp. 1203-1219
    • Lieberman, G.M.1
  • 22
    • 0037778705 scopus 로고    scopus 로고
    • A mostly elementary proof of Morrey space estimates for elliptic and parabolic equations with VMO coefficients
    • Lieberman G.M. A mostly elementary proof of Morrey space estimates for elliptic and parabolic equations with VMO coefficients. J. Funct. Anal. 201 2 (2003) 457-479
    • (2003) J. Funct. Anal. , vol.201 , Issue.2 , pp. 457-479
    • Lieberman, G.M.1
  • 23
    • 0000028675 scopus 로고
    • Quasilinear elliptic equations with VMO coefficients
    • Palagachev D.K. Quasilinear elliptic equations with VMO coefficients. Trans. Amer. Math. Soc. 347 7 (1995) 2481-2493
    • (1995) Trans. Amer. Math. Soc. , vol.347 , Issue.7 , pp. 2481-2493
    • Palagachev, D.K.1
  • 24
    • 51249192844 scopus 로고
    • Solutions of the Plateau problem for m-dimensional surfaces of varying topological type
    • Reifenberg E. Solutions of the Plateau problem for m-dimensional surfaces of varying topological type. Acta Math. 104 (1960) 1-92
    • (1960) Acta Math. , vol.104 , pp. 1-92
    • Reifenberg, E.1
  • 25
    • 0009320957 scopus 로고
    • Harnack's inequality for elliptic equations and Hölder property of their solutions
    • 312
    • Safonov M.V. Harnack's inequality for elliptic equations and Hölder property of their solutions. Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 96 (1980) 272-287 312
    • (1980) Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) , vol.96 , pp. 272-287
    • Safonov, M.V.1
  • 26
    • 84946916764 scopus 로고
    • Functions of vanishing mean oscillation
    • Sarason D. Functions of vanishing mean oscillation. Trans. Amer. Math. Soc. 207 (1975) 391-405
    • (1975) Trans. Amer. Math. Soc. , vol.207 , pp. 391-405
    • Sarason, D.1
  • 27
    • 0004136765 scopus 로고
    • Princeton Univ. Press, Princeton, NJ
    • Stein E.M. Harmonic Analysis (1993), Princeton Univ. Press, Princeton, NJ
    • (1993) Harmonic Analysis
    • Stein, E.M.1
  • 28
    • 33846445540 scopus 로고
    • Regularity for a more general class of quasilinear elliptic equations
    • Tolksdorf P. Regularity for a more general class of quasilinear elliptic equations. J. Differential Equations 51 1 (1984) 126-150
    • (1984) J. Differential Equations , vol.51 , Issue.1 , pp. 126-150
    • Tolksdorf, P.1
  • 29
    • 0039455568 scopus 로고    scopus 로고
    • Doubling and flatness: Geometry of measures
    • Toro T. Doubling and flatness: Geometry of measures. Notices Amer. Math. Soc. (1997) 1087-1094
    • (1997) Notices Amer. Math. Soc. , pp. 1087-1094
    • Toro, T.1
  • 30
    • 0000968617 scopus 로고
    • Regularity for a class of non-linear elliptic systems
    • Uhlenbeck K. Regularity for a class of non-linear elliptic systems. Acta Math. 138 (1977) 219-240
    • (1977) Acta Math. , vol.138 , pp. 219-240
    • Uhlenbeck, K.1


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