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Modulus of continuity of harmonic functions

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Abstract

LetG be a bounded plane domain, the diameters of whose boundary components have a fixed positive lower bound. Letu be harmonic inG and continuous in the closureG ofG. Suppose that the modulus of continuity ofu on the boundary ofG is majorized by a function of a suitable type. We shall then obtain upper bounds for the modulus of continuity ofu inG. Further, we shall show that in some situations these estimates cannot be essentially improved. We shall also consider the same problem for certain bounded domains in space.

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Author notes

  1. A. Hinkkanen

    Present address: Department of Mathematics, University of Texas at Austin, 78712, Austin, TX, USA

Authors and Affiliations

  1. Department of Mathematics, University of Michigan, 48109-1003, Ann Arbor, MI, USA

    A. Hinkkanen

Authors
  1. A. Hinkkanen
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Additional information

Research partially supported by the U.S. National Science Foundation. AMS (1980) Classification. Primary 31A05.

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Hinkkanen, A. Modulus of continuity of harmonic functions. J. Anal. Math. 51, 1–29 (1988). https://doi.org/10.1007/BF02791117

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  • DOI: https://doi.org/10.1007/BF02791117

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