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Parabolic Equations in Reifenberg Domains

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Abstract.

Natural Sobolev-type estimates are proved for weak solutions of inhomogeneous parabolic equations in divergence form in a bounded cylinder Ω*=Ω×(0,T] which is δ-Reifenberg flat in the space direction. The principal coefficients of the operator are assumed to be in BMO space with their BMO semi-norms small enough.

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Authors and Affiliations

  1. Department of Mathematics, Seoul National University, Seoul, 151–747, Korea

    Sun-Sig Byun

  2. Department of Mathematics, University of Iowa, Iowa City, IA, 52242, USA

    Lihe Wang

  3. College of Sciences, Xian Jiaotong University, Xian, 710049, China

    Lihe Wang

Authors
  1. Sun-Sig Byun
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  2. Lihe Wang
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Communicated by L.C. Evans

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Byun, SS., Wang, L. Parabolic Equations in Reifenberg Domains. Arch. Rational Mech. Anal. 176, 271–301 (2005). https://doi.org/10.1007/s00205-005-0357-6

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  • DOI: https://doi.org/10.1007/s00205-005-0357-6

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