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Partial Differential Equations with Minimal Smoothness and Applications pp 89–97Cite as

Some Questions Concerning Harmonic Measure

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Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 42))

Abstract

The purpose of this note is to discuss some conjectures concerning harmonic measure. We will start by considering harmonic measure on a simply connected plane domain Ω, but eventually we will also consider some multiply connected and higher dimensional domains. Most of these questions are trivial if ∂Ω has tangents a.e. and many are easy if Ω is only a quasicircle. Thus they are really questions about very non-smooth domains.

The author is partially supported by an NSF Postdoctoral Fellowship

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Author information

Authors and Affiliations

  1. Dept. of Mathematics, UCLA, USA

    Christopher J. Bishop

Authors
  1. Christopher J. Bishop
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of South Carolina, Columbia, SC, 29303, USA

    B. Dahlberg

  2. Department of Mathematics, University of Chicago, Chicago, IL, 60637, USA

    R. Fefferman , Carlos Kenig  & J. Pipher ,  & 

  3. Department of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA

    Eugene Fabes

  4. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    David Jerison

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© 1992 Springer-Verlag New York, Inc.

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Bishop, C.J. (1992). Some Questions Concerning Harmonic Measure. In: Dahlberg, B., Fefferman, R., Kenig, C., Fabes, E., Jerison, D., Pipher, J. (eds) Partial Differential Equations with Minimal Smoothness and Applications. The IMA Volumes in Mathematics and its Applications, vol 42. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2898-1_7

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  • DOI: https://doi.org/10.1007/978-1-4612-2898-1_7

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7712-5

  • Online ISBN: 978-1-4612-2898-1

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