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Boundary Harnack Principle for p-harmonic Functions in Smooth Euclidean Domains

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Abstract

We establish a scale-invariant version of the boundary Harnack principle for p-harmonic functions in Euclidean C 1,1-domains and obtain estimates for the decay rates of positive p-harmonic functions vanishing on a segment of the boundary in terms of the distance to the boundary. We use these estimates to study the behavior of conformal Martin kernel functions and positive p-superharmonic functions near the boundary of the domain.

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Authors and Affiliations

  1. Department of Mathematics, Hokkaido University, 060-0810, Sapporo, Japan

    Hiroaki Aikawa

  2. Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35 (MaD), 40014, University of Jyväskylä, Finland

    Tero Kilpeläinen & Xiao Zhong

  3. Department of Mathematical Sciences, University of Cincinnati, P.O. Box 210025, Cincinnati, OH, 45221–0025, USA

    Nageswari Shanmugalingam

Authors
  1. Hiroaki Aikawa
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  2. Tero Kilpeläinen
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  3. Nageswari Shanmugalingam
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  4. Xiao Zhong
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Corresponding author

Correspondence to Hiroaki Aikawa.

Additional information

H. A. was partially supported by Grant-in-Aid for (B) (2) (No. 15340046) Japan Society for the Promotion of Science. N. S. was partially supported by NSF grant DMS-0355027. X. Z. was partially supported by the Taft foundation.

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Aikawa, H., Kilpeläinen, T., Shanmugalingam, N. et al. Boundary Harnack Principle for p-harmonic Functions in Smooth Euclidean Domains. Potential Anal 26, 281–301 (2007). https://doi.org/10.1007/s11118-006-9036-y

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  • DOI: https://doi.org/10.1007/s11118-006-9036-y

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