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Hölder Regularity of Solutions to Second-Order Elliptic Equations in Nonsmooth Domains

Boundary Value Problems volume 2007, Article number: 057928 (2006) Cite this article

Abstract

We establish the global Hölder estimates for solutions to second-order elliptic equations, which vanish on the boundary, while the right-hand side is allowed to be unbounded. For nondivergence elliptic equations in domains satisfying an exterior cone condition, similar results were obtained by J. H. Michael, who in turn relied on the barrier techniques due to K. Miller. Our approach is based on special growth lemmas, and it works for both divergence and nondivergence, elliptic and parabolic equations, in domains satisfying a general "exterior measure" condition.

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Authors and Affiliations

  1. Department of Mathematics, Michigan State University, East Lansing, MI, 48824, USA

    Sungwon Cho

  2. School of Mathematics, University of Minnesota, 127 Vincent Hall, Minneapolis, MN, 55455, USA

    Mikhail Safonov

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  1. Sungwon Cho
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  2. Mikhail Safonov
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Correspondence to Sungwon Cho.

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Cho, S., Safonov, M. Hölder Regularity of Solutions to Second-Order Elliptic Equations in Nonsmooth Domains. Bound Value Probl 2007, 057928 (2006). https://doi.org/10.1155/2007/57928

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Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Equation
  • Special Growth