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Volumn 199, Issue 3, 2011, Pages 889-941

On the Lp-Solvability of Higher Order Parabolic and Elliptic Systems with BMO Coefficients

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EID: 79951813420     PISSN: 00039527     EISSN: 14320673     Source Type: Journal    
DOI: 10.1007/s00205-010-0345-3     Document Type: Article
Times cited : (113)

References (37)
  • 1
    • 0003924563 scopus 로고    scopus 로고
    • Prepared for publication by B. Frank Jones, Jr. with the assistance of George W. Batten, Jr. Revised edition of the 1965 original. AMS Chelsea Publishing, Providence, RI
    • Agmon, S.: Lectures on Elliptic Boundary Value Problems. Prepared for publication by B. Frank Jones, Jr. with the assistance of George W. Batten, Jr. Revised edition of the 1965 original. AMS Chelsea Publishing, Providence, RI, 2010.
    • (2010) Lectures On Elliptic Boundary Value Problems
    • Agmon, S.1
  • 2
    • 84980075953 scopus 로고
    • Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, I
    • Agmon S., Douglis A., Nirenberg L.: Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, I. Commun. Pure Appl. Math. 12, 623-727 (1959).
    • (1959) Commun. Pure Appl. Math. , vol.12 , pp. 623-727
    • Agmon, S.1    Douglis, A.2    Nirenberg, L.3
  • 3
    • 84980080664 scopus 로고
    • Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, II
    • Agmon S., Douglis A., Nirenberg L.: Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, II. Commun. Pure Appl. Math. 17, 35-92 (1964).
    • (1964) Commun. Pure Appl. Math. , vol.17 , pp. 35-92
    • Agmon, S.1    Douglis, A.2    Nirenberg, L.3
  • 5
    • 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. Commun. Partial Differ. Equ. 18(9-10), 1735-1763 (1993).
    • (1993) Commun. Partial Differ. Equ. , vol.18 , Issue.9-10 , pp. 1735-1763
    • Bramanti, M.1    Cerutti, M.2
  • 6
    • 4544307605 scopus 로고    scopus 로고
    • Elliptic equations with BMO coefficients in Reifenberg domains
    • Byun S., Wang L.: Elliptic equations with BMO coefficients in Reifenberg domains. Commun. Pure Appl. Math. 57(10), 1283-1310 (2004).
    • (2004) Commun. Pure Appl. Math. , vol.57 , Issue.10 , pp. 1283-1310
    • Byun, S.1    Wang, L.2
  • 7
    • 63149100910 scopus 로고    scopus 로고
    • Hessian estimates in Orlicz spaces for fourth-order parabolic systems in non-smooth domains
    • Byun S.: Hessian estimates in Orlicz spaces for fourth-order parabolic systems in non-smooth domains. J. Differ. Equ. 246(9), 3518-3534 (2009).
    • (2009) J. Differ. Equ. , vol.246 , Issue.9 , pp. 3518-3534
    • Byun, S.1
  • 8
    • 0000427184 scopus 로고
    • 2,p estimates for nondivergence elliptic equations with discontinuous coefficients
    • 2, p estimates for nondivergence elliptic equations with discontinuous coefficients. Ricerche Mat. 40, 149-168 (1991).
    • (1991) Ricerche Mat. , vol.40 , pp. 149-168
    • Chiarenza, F.1    Frasca, M.2    Longo, P.3
  • 9
    • 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. Am. Math. Soc. 336(2), 841-853 (1993).
    • (1993) Trans. Am. Math. Soc. , vol.336 , Issue.2 , pp. 841-853
    • Chiarenza, F.1    Frasca, M.2    Longo, P.3
  • 11
    • 1542782912 scopus 로고    scopus 로고
    • p estimates for divergence form elliptic equations with discontinuous coefficients. (Italian summary)
    • p estimates for divergence form elliptic equations with discontinuous coefficients. (Italian summary). Boll. Un. Mat. Ital. A (7) 10(2), 409-420 (1996).
    • (1996) Boll. Un. Mat. Ital. A (7) , vol.10 , Issue.2 , pp. 409-420
    • Di Fazio, G.1
  • 12
    • 79951811135 scopus 로고    scopus 로고
    • Solvability of second-order equations with hierarchically partially BMO coefficients, submitted
    • Dong, H.: Solvability of second-order equations with hierarchically partially BMO coefficients, submitted (2009).
    • (2009)
    • Dong, H.1
  • 13
    • 77950023577 scopus 로고    scopus 로고
    • Elliptic equations in divergence form with partially BMO coefficients
    • Dong H., Kim D.: Elliptic equations in divergence form with partially BMO coefficients. Arch. Ration. Mech. Anal. 196(1), 25-70 (2010).
    • (2010) Arch. Ration. Mech. Anal. , vol.196 , Issue.1 , pp. 25-70
    • Dong, H.1    Kim, D.2
  • 14
    • 78751583946 scopus 로고    scopus 로고
    • Parabolic and elliptic systems with VMO coefficients
    • Dong H., Kim D.: Parabolic and elliptic systems with VMO coefficients. Methods Appl. Anal. 16(3), 365-388 (2009).
    • (2009) Methods Appl. Anal. , vol.16 , Issue.3 , pp. 365-388
    • Dong, H.1    Kim, D.2
  • 15
    • 79951810125 scopus 로고    scopus 로고
    • Lp solvability of divergence type parabolic and elliptic systems with partially BMO coefficients
    • to appear
    • Dong, H., Kim, D.: Lp solvability of divergence type parabolic and elliptic systems with partially BMO coefficients. Calc. Var. Partial Differ. Equ. (2010, to appear).
    • (2010) Calc. Var. Partial Differ. Equ
    • Dong, H.1    Kim, D.2
  • 16
    • 0036678331 scopus 로고    scopus 로고
    • 2-regularity theory of linear strongly elliptic Dirichlet systems of order 2m with minimal regularity in the coefficients
    • 2-regularity theory of linear strongly elliptic Dirichlet systems of order 2m with minimal regularity in the coefficients. Q. Appl. Math. 60(3), 547-576 (2002).
    • (2002) Q. Appl. Math. , vol.60 , Issue.3 , pp. 547-576
    • Ebenfeld, S.1
  • 20
    • 0040335288 scopus 로고
    • Introduction to Regularity Theory for Nonlinear Elliptic Systems
    • Birkhäuser Verlag, Basel
    • Giaquinta, M.: Introduction to Regularity Theory for Nonlinear Elliptic Systems. Lectures in Mathematics ETH Zürich. Birkhäuser Verlag, Basel, 1993.
    • (1993) Lectures In Mathematics ETH Zürich
    • Giaquinta, M.1
  • 22
    • 33846046441 scopus 로고    scopus 로고
    • q-estimates for parabolic systems in non-divergence form with VMO coefficients
    • q-estimates for parabolic systems in non-divergence form with VMO coefficients. J. Lond. Math. Soc. (2) 74(3), 717-736 (2006).
    • (2006) J. Lond. Math. Soc. (2) , vol.74 , Issue.3 , pp. 717-736
    • Haller-Dintelmann, R.1    Heck, H.2    Hieber, M.3
  • 23
    • 41449093759 scopus 로고    scopus 로고
    • Elliptic differential equations with coefficients measurable with respect to one variable and VMO with respect to the others
    • Kim D., Krylov N. V.: Elliptic differential equations with coefficients measurable with respect to one variable and VMO with respect to the others. SIAM J. Math. Anal. 39(2), 489-506 (2007).
    • (2007) SIAM J. Math. Anal. , vol.39 , Issue.2 , pp. 489-506
    • Kim, D.1    Krylov, N.V.2
  • 24
    • 34247390646 scopus 로고    scopus 로고
    • Parabolic equations with measurable coefficients
    • Kim D., Krylov N. V.: Parabolic equations with measurable coefficients. Potential Anal. 26(4), 345-361 (2007).
    • (2007) Potential Anal. , vol.26 , Issue.4 , pp. 345-361
    • Kim, D.1    Krylov, N.V.2
  • 25
    • 33947167707 scopus 로고    scopus 로고
    • Parabolic and elliptic equations with VMO coefficients
    • Krylov N. V.: Parabolic and elliptic equations with VMO coefficients. Commun. Partial Differ. Equ. 32(1-3), 453-475 (2007).
    • (2007) Commun. Partial Differ. Equ. , vol.32 , Issue.1-3 , pp. 453-475
    • Krylov, N.V.1
  • 26
    • 34547701915 scopus 로고    scopus 로고
    • Parabolic equations with VMO coefficients in spaces with mixed norms
    • Krylov N. V.: Parabolic equations with VMO coefficients in spaces with mixed norms. J. Funct. Anal. 250(2), 521-558 (2007).
    • (2007) J. Funct. Anal. , vol.250 , Issue.2 , pp. 521-558
    • Krylov, N.V.1
  • 28
    • 67650089622 scopus 로고    scopus 로고
    • Second-order elliptic equations with variably partially VMO coefficients
    • Krylov N. V.: Second-order elliptic equations with variably partially VMO coefficients. J. Funct. Anal. 257, 1695-1712 (2009).
    • (2009) J. Funct. Anal. , vol.257 , pp. 1695-1712
    • Krylov, N.V.1
  • 30
    • 12444265748 scopus 로고    scopus 로고
    • Hölder regularity of the solutions of some classes of elliptic systems in convex nonsmooth domains
    • Leonardi S., Kottas J., Stara J.: Hölder regularity of the solutions of some classes of elliptic systems in convex nonsmooth domains. Nonlinear Anal. 60, 925-944 (2005).
    • (2005) Nonlinear Anal. , vol.60 , pp. 925-944
    • Leonardi, S.1    Kottas, J.2    Stara, J.3
  • 32
    • 10844283460 scopus 로고    scopus 로고
    • Elliptic and Parabolic Equations with Discontinuous Coefficients
    • Wiley-VCH, Berlin
    • Maugeri, A., Palagachev, D., Softova, L.: Elliptic and Parabolic Equations with Discontinuous Coefficients, Math. Res., vol. 109. Wiley-VCH, Berlin, 2000.
    • (2000) Math. Res , vol.109
    • Maugeri, A.1    Palagachev, D.2    Softova, L.3
  • 33
    • 33748256093 scopus 로고    scopus 로고
    • 1 or Lipschitz domains
    • 1 or Lipschitz domains. J. Differ. Equ. 230(1), 174-195 (2006).
    • (2006) J. Differ. Equ. , vol.230 , Issue.1 , pp. 174-195
    • Miyazaki, Y.1
  • 34
    • 23844450455 scopus 로고    scopus 로고
    • A priori estimates and precise regularity for parabolic systems with discontinuous data
    • Palagachev D., Softova L.: A priori estimates and precise regularity for parabolic systems with discontinuous data. Discrete Contin. Dyn. Syst. 13(3), 721-742 (2005).
    • (2005) Discrete Contin. Dyn. Syst. , vol.13 , Issue.3 , pp. 721-742
    • Palagachev, D.1    Softova, L.2
  • 35
    • 79951809153 scopus 로고    scopus 로고
    • Precise regularity of solutions to elliptic systems with discontinuous data
    • no. 2
    • Palagachev, D., Softova, L.: Precise regularity of solutions to elliptic systems with discontinuous data. Ricerche Mat. 54 (2005), no. 2, 631-639 (2006).
    • (2006) Ricerche Mat , vol.54 , Issue.2005 , pp. 631-639
    • Palagachev, D.1    Softova, L.2
  • 36
    • 0002042250 scopus 로고
    • On boundary value problems for linear parabolic systems of differential equations of general form, (Russian)
    • Solonnikov, V. A.: On boundary value problems for linear parabolic systems of differential equations of general form, (Russian), Trudy Mat. Inst. Steklov. 83, 3-163 (1965)
    • (1965) Trudy Mat. Inst. Steklov. , vol.83 , pp. 3-163
    • Solonnikov, V.A.1
  • 37
    • 79951813602 scopus 로고
    • English translation: Proceedings of the Steklov Institute of Mathematics. No. 83:, Boundary value problems of mathematical physics. III. Edited by O. A. Ladyženskaja. Translated from the Russian by A. Jablonskiǐ, American Mathematical Society, Providence, R. I. 1967
    • English translation: Proceedings of the Steklov Institute of Mathematics. No. 83 (1965): Boundary value problems of mathematical physics. III. Edited by O. A. Ladyženskaja. Translated from the Russian by A. Jablonskiǐ, American Mathematical Society, Providence, R. I. 1967 iv+184 pp.
    • (1965)


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