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Calderón-Zygmund estimate for homogenization of parabolic systems

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  • We establish a global Calderón-Zygmund estimate for homogenization of a parabolic system in divergence form with discontinuous coefficients in a bounded nonsmooth domain under the assumptions that the coefficients have small BMO seminorms and the boundary of the domain is $\delta$-flat for some $\delta>0$ depending on the given data.
    Mathematics Subject Classification: 35K40, 35B65, 35B27.


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  • [1]

    M. Avellaneda and F. Lin, Compactness methods in the theory of homogenization, Comm. Pure Appl. Math., 40 (1987), 803-847.doi: 10.1002/cpa.3160400607.


    A. Bensoussan, J. L. Lions and G. Papanicolaou, Asymptotic Analysis for Periodic Structures, AMS Chelsea Publishing, Providence, RI, 2011.doi: 10.1090/chel/374.


    S. Byun and L. Wang, Parabolic equations in Reifenberg domains, Arch. Ration. Mech. Anal., 176 (2005), 271-301.doi: 10.1007/s00205-005-0357-6.


    S. Byun and S. Ryu, Global estimates in Orlicz spaces for the gradient of solutions to parabolic systems, Proc. Amer. Math. Soc., 138 (2010), 641-653.doi: 10.1090/S0002-9939-09-10094-1.


    V. Bögelein and M. Parviainen, Self-improving property of nonlinear higher order parabolic systems near the boundary, NoDEA Nonlinear Differential Equations Appl., 17 (2010), 21-54.doi: 10.1007/s00030-009-0038-5.


    L. A. Caffarelli and X. Cabré, Fully Nonlinear Elliptic Equations, American Mathematical Society Colloquium Publications, 43. American Mathematical Society, Providence, RI, 1995.doi: 10.1090/coll/043.


    L. A. Caffarelli and I. Peral, On $W^{1,p}$ estimates for elliptic equations in divergence form, Comm. Pure Appl. Math., 51 (1998), 1-21.doi: 10.1002/(SICI)1097-0312(199801)51:1<1::AID-CPA1>3.0.CO;2-G.


    E. DiBenedetto, Degenerate Parabolic Equations, Universitext. Springer-Verlag, New York, 1993. xvi+387 pp.doi: 10.1007/978-1-4612-0895-2.


    J. Geng and Z. Shen, Uniform regularity estimates in parabolic homogenization, Indiana Univ. Math. J., 64 (2015), 697-733.doi: 10.1512/iumj.2015.64.5503.


    E. R. Reifenberg, Solution of the Plateau Problem for m -dimensional surfaces of varying topological type, Acta Math., 104 (1960), 1-92.doi: 10.1007/BF02547186.


    T. Toro, Doubling and flatness: geometry of measures, Notices Amer. Math. Soc., 44 (1997), 1087-1094.


    L. Wang, A geometric approach to the Calderón-Zygmund estimates, Acta Math. Sin. (Engl. Ser.), 19 (2003), 381-396.doi: 10.1007/s10114-003-0264-4.

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