Journal d’Analyse Mathématique

, Volume 85, Issue 1, pp 339–369 | Cite as

Fat sets and pointwise boundary estimates forp-harmonic functions in metric spaces

  • Jana Björn
  • Paul MacManus
  • Nageswari Shanmugalingam


We extend a result of John Lewis [L] by showing that if a doubling metric measure space supports a (1,q 0)-Poincaré inequality for some 1<q 0<p, then every uniformlyp-fat set is uniformlyq-fat for someq<p. This bootstrap result implies the Hardy inequality for Newtonian functions with zero boundary values for domains whose complements are uniformly fat. While proving this result, we also characterize positive Radon measures in the dual of the Newtonian space using the Wolff potential and obtain an estimate for the oscillation ofp-harmonic functions andp-energy minimizers near a boundary point.


Sobolev Inequality Radon Measure Harnack Inequality Hardy Inequality Strong Maximum Principle 
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Copyright information

© The Hebrew University Magnes Press 2001

Authors and Affiliations

  • Jana Björn
    • 1
  • Paul MacManus
    • 2
  • Nageswari Shanmugalingam
    • 3
  1. 1.Department of MathematicsLund Institute of TechnologyLundSweden
  2. 2.Department of MathematicsPhillips Exeter AcademyExeterUSA
  3. 3.Department of MathematicsUniversity of Texas at AustinAustinUSA

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