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Volumn 223, Issue 1, 2005, Pages 44-85

Lp estimates for parabolic equations in Reifenberg domains

Author keywords

Maximal function; Reifenberg flat domain; Vitali covering lemma

Indexed keywords


EID: 17844373003     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jfa.2004.10.014     Document Type: Article
Times cited : (20)

References (43)
  • 1
    • 0001430761 scopus 로고
    • On BMO regularity for linear elliptic systems
    • P. Acquistapace On BMO regularity for linear elliptic systems Ann. Mat. Pura Appl. 161 1992 231-269
    • (1992) Ann. Mat. Pura Appl. , vol.161 , pp. 231-269
    • Acquistapace, P.1
  • 3
    • 0011048676 scopus 로고
    • Problemi misti per l'equazione del calore
    • C. Baiocchi Problemi misti per l'equazione del calore Rend. Sem. Mat. Fis. Milano 41 1971 15-54
    • (1971) Rend. Sem. Mat. Fis. Milano , vol.41 , pp. 15-54
    • Baiocchi, C.1
  • 4
    • 84871414400 scopus 로고
    • 1,2 solvability for the Cauchy-Dirichlet problem for parabolic equations with VMO coefficients
    • 1,2 solvability for the Cauchy-Dirichlet problem for parabolic equations with VMO coefficients Comm. Partial Differential Equations 18 1993 1735-1763
    • (1993) Comm. Partial Differential Equations , vol.18 , pp. 1735-1763
    • Bramanti, M.1    Cerutti, M.C.2
  • 5
    • 14844329076 scopus 로고    scopus 로고
    • Elliptic equations with BMO coefficents in Lipschitz domains
    • S. Byun Elliptic equations with BMO coefficents in Lipschitz domains Trans. Amer. Math. Soc. 357 2005 1025-1046
    • (2005) Trans. Amer. Math. Soc. , vol.357 , pp. 1025-1046
    • Byun, S.1
  • 6
    • 11144322175 scopus 로고    scopus 로고
    • Parabolic equations with BMO coefficients in Lipschitz domains
    • S. Byun Parabolic equations with BMO coefficients in Lipschitz domains J. Differential Equations 209 2005 229-265
    • (2005) J. Differential Equations , vol.209 , pp. 229-265
    • Byun, S.1
  • 7
    • 4544307605 scopus 로고    scopus 로고
    • Elliptic equations with BMO coefficients in Reifenberg domains
    • S. Byun L. Wang 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
  • 8
    • 17744369923 scopus 로고    scopus 로고
    • The conormal derivative problem for elliptic equations with BMO coefficients on Reifenberg flat domains
    • S. Byun L. Wang The conormal derivative problem for elliptic equations with BMO coefficients on Reifenberg flat domains Proc. London Math. Soc. (3) 90 1 2005 247-272
    • (2005) Proc. London Math. Soc. (3) , vol.90 , Issue.1 , pp. 247-272
    • Byun, S.1    Wang, L.2
  • 11
    • 0000427184 scopus 로고
    • 2,pM estimates for nondivergence elliptic equations with discontinuous coefficients
    • 2,p estimates for nondivergence elliptic equations with discontinuous coefficients Ricerche Mat. 40 1991 149-168
    • (1991) Ricerche Mat. , vol.40 , pp. 149-168
    • Chiarenza, F.1    Frasca, M.2    Longo, P.3
  • 12
    • 0001569352 scopus 로고
    • 2,p-solvability of the Dirichlet problem for nondivergence elliptic equations with VMO coefficients
    • 2,p-solvability of the Dirichlet problem for nondivergence elliptic equations with VMO coefficients Trans. Amer. Math. Soc. 336 1993 841-853
    • (1993) Trans. Amer. Math. Soc. , vol.336 , pp. 841-853
    • Chiarenza, F.1    Frasca, M.2    Longo, P.3
  • 13
    • 0035586323 scopus 로고    scopus 로고
    • Asymptotically optimally doubling measures and Reifenberg flat sets with vanishing constant
    • G. David C. Kenig T. Toro Asymptotically optimally doubling measures and Reifenberg flat sets with vanishing constant Comm. Pure. Appl. Math. 54 2001 385-449
    • (2001) Comm. Pure. Appl. Math. , vol.54 , pp. 385-449
    • David, G.1    Kenig, C.2    Toro, T.3
  • 14
    • 22844453615 scopus 로고    scopus 로고
    • Reifenberg flat metric spaces, snowballs, and embeddings
    • G. David T. Toro Reifenberg flat metric spaces, snowballs, and embeddings Math. Ann. 315 1999 641-710
    • (1999) Math. Ann. , vol.315 , pp. 641-710
    • David, G.1    Toro, T.2
  • 15
    • 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. Un. Mat. Ital. A(7) 10 1996 409-420
    • (1996) Boll. Un. Mat. Ital. A(7) , vol.10 , pp. 409-420
    • Di Fazio, G.1
  • 17
    • 0030642447 scopus 로고    scopus 로고
    • Traces of Sobolev functions on fractal type sets and characterization of extension domains
    • P. Hajlasz O. Martio Traces of Sobolev functions on fractal type sets and characterization of extension domains J. Func. Anal. 143 1997 221-246
    • (1997) J. Func. Anal. , vol.143 , pp. 221-246
    • Hajlasz, P.1    Martio, O.2
  • 18
    • 84975506572 scopus 로고    scopus 로고
    • Sobolev extension domains on metric spaces of homogeneous type
    • P. Harjulehto Sobolev extension domains on metric spaces of homogeneous type Real Anal. Exchange 27 2001 583-597
    • (2001) Real Anal. Exchange , vol.27 , pp. 583-597
    • Harjulehto, P.1
  • 21
    • 84980082306 scopus 로고
    • On functions of bounded mean oscillation
    • F. John L. Nirenberg 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
  • 22
    • 0003016779 scopus 로고
    • Extension theorems for BMO
    • P.W. Jones Extension theorems for BMO Indiana Univ. Math. J. 29 1980 41-66
    • (1980) Indiana Univ. Math. J. , vol.29 , pp. 41-66
    • Jones, P.W.1
  • 23
    • 0002428795 scopus 로고
    • Quasiconformal mappings and extendability of functions in Sobolev spaces
    • P.W. Jones 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
  • 24
    • 1842780203 scopus 로고    scopus 로고
    • Flatness of domains and doubling properties of measures supported on their boundary, with applications to harmonic measure
    • C. Kenig Flatness of domains and doubling properties of measures supported on their boundary, with applications to harmonic measure J. Fourier Anal. Appl. 3 1997 923-931
    • (1997) J. Fourier Anal. Appl. , vol.3 , pp. 923-931
    • Kenig, C.1
  • 25
    • 0033235413 scopus 로고    scopus 로고
    • Free boundary regularity for harmonic measures and the Poisson kernel
    • C. Kenig T. Toro Free boundary regularity for harmonic measures and the Poisson kernel Ann. Math. 150 1999 367-454
    • (1999) Ann. Math. , vol.150 , pp. 367-454
    • Kenig, C.1    Toro, T.2
  • 26
    • 0036322657 scopus 로고    scopus 로고
    • Free boundary regularity for the Poisson kernel below the continuous threshold
    • C. Kenig T. Toro Free boundary regularity for the Poisson kernel below the continuous threshold Math. Res. Lett. 54 2002 247-253
    • (2002) Math. Res. Lett. , vol.54 , pp. 247-253
    • Kenig, C.1    Toro, T.2
  • 28
    • 0037778705 scopus 로고    scopus 로고
    • A mostly elementary proof of Morrey space estimates for elliptic and parabolic equations with VMO coefficients
    • G.M. Lieberman A mostly elementary proof of Morrey space estimates for elliptic and parabolic equations with VMO coefficients J. Funct. Anal. 201 2003 457-479
    • (2003) J. Funct. Anal. , vol.201 , pp. 457-479
    • Lieberman, G.M.1
  • 29
    • 0039145521 scopus 로고
    • Hölder continuity of the gradient of solutions of uniformly parabolic equations with conormal boundary conditions
    • G.M. Lieberman Hölder continuity of the gradient of solutions of uniformly parabolic equations with conormal boundary conditions Ann. Mat. Pura Appl. (4) 148 1987 77-99
    • (1987) Ann. Mat. Pura Appl. (4) , vol.148 , pp. 77-99
    • Lieberman, G.M.1
  • 30
    • 0004808534 scopus 로고
    • The conormal derivative problem for nonuniformly parabolic equations
    • G.M. Lieberman The conormal derivative problem for nonuniformly parabolic equations Indiana Univ. Math. J. 37 1988 23-72
    • (1988) Indiana Univ. Math. J. , vol.37 , pp. 23-72
    • Lieberman, G.M.1
  • 31
    • 8844242627 scopus 로고
    • The conormal derivative problem for equations of variational type in nonsmooth domains
    • G.M. Lieberman The conormal derivative problem for equations of variational type in nonsmooth domains Trans. Amer. Math. Soc. 330 1992 41-67
    • (1992) Trans. Amer. Math. Soc. , vol.330 , pp. 41-67
    • Lieberman, G.M.1
  • 33
    • 0010990815 scopus 로고
    • Problemi al contorno misti per l'equazione del calore
    • (Italian)
    • E. Magenes Problemi al contorno misti per l'equazione del calore (Italian) Rend. Sem. Mat. Univ. Padova 24 1955 1-28
    • (1955) Rend. Sem. Mat. Univ. Padova , vol.24 , pp. 1-28
    • Magenes, E.1
  • 34
    • 0003265439 scopus 로고
    • Geometry of sets and measures in Euclidean spaces, Fractals and rectifiability
    • Cambridge University Press, Cambridge xii+343
    • P. Mattila, Geometry of sets and measures in Euclidean spaces, Fractals and rectifiability, Cambridge Studies in Advanced Mathematics, vol. 44, Cambridge University Press, Cambridge, 1995, xii+343pp.
    • (1995) Cambridge Studies in Advanced Mathematics , vol.44
    • Mattila, P.1
  • 35
    • 10844283460 scopus 로고    scopus 로고
    • Elliptic and parabolic equations with discontinuous coefficients
    • Wiley-VCH Berlin
    • A. Maugeri D.K. Palagachev L.G. Softova Elliptic and parabolic equations with discontinuous coefficients Mathematical Research vol. 109 2000 Wiley-VCH Berlin
    • (2000) Mathematical Research , vol.109
    • Maugeri, A.1    Palagachev, D.K.2    Softova, L.G.3
  • 36
    • 51249192844 scopus 로고
    • Solutions of the plateau problem for m-dimensional surfaces of varying topological type
    • E. Reinfenberg Solutions of the plateau problem for m-dimensional surfaces of varying topological type J. Funct. Anal. 1960 1-92
    • (1960) J. Funct. Anal. , pp. 1-92
    • Reinfenberg, E.1
  • 37
    • 84946916764 scopus 로고
    • Functions of vanishing mean oscillation
    • D. Sarason 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
  • 38
    • 0034356650 scopus 로고    scopus 로고
    • Oblique derivative problem for parabolic operators with VMO coefficients
    • L.G. Softova Oblique derivative problem for parabolic operators with VMO coefficients Manuscripte Math. 103 2000 203-220
    • (2000) Manuscripte Math. , vol.103 , pp. 203-220
    • Softova, L.G.1
  • 39
    • 4544223607 scopus 로고    scopus 로고
    • Quasilinear parabolic equations with VMO coefficients
    • L.G. Softova Quasilinear parabolic equations with VMO coefficients C. R. Acad. Bulgare Sci. 53 2000 17-20
    • (2000) C. R. Acad. Bulgare Sci. , vol.53 , pp. 17-20
    • Softova, L.G.1
  • 40
    • 52549116250 scopus 로고    scopus 로고
    • Parabolic equations with VMO coefficients in Morrey spaces
    • L.G. Softova Parabolic equations with VMO coefficients in Morrey spaces Electron. J. Differential Equations 51 2001 1-25
    • (2001) Electron. J. Differential Equations , vol.51 , pp. 1-25
    • Softova, L.G.1
  • 41
    • 0004136765 scopus 로고
    • Princeton, NJ: Princeton University Press
    • E.M. Stein Harmonic Analysis 1993 Princeton University Press Princeton, NJ
    • (1993) Harmonic Analysis
    • Stein, E.M.1
  • 42
    • 0039455568 scopus 로고    scopus 로고
    • Doubling and flatness: Geometry of measures
    • T. Toro Doubling and flatness geometry of measures Notices Amer. Math. Soc. 44 1997 1087-1094
    • (1997) Notices Amer. Math. Soc. , vol.44 , pp. 1087-1094
    • Toro, T.1
  • 43
    • 1442280649 scopus 로고    scopus 로고
    • A geometric approach to the Calderón-Zygmund estimates
    • L. Wang A geometric approach to the Calderón-Zygmund estimates Acta Math. Sinica 19 2003 381-396
    • (2003) Acta Math. Sinica , vol.19 , pp. 381-396
    • Wang, L.1


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