On p-harmonic measures in half-spaces

  • José G. LlorenteEmail author
  • Juan J. Manfredi
  • William C. Troy
  • Jang-Mei Wu


For all \(1<p<\infty \) and \(N\ge 2\) we prove by using ODE shooting techniques that there is a constant \(\alpha (p,N)>0\) such that the p-harmonic measure in \({\mathbb {R}}^N_+\) of a ball of radius \(0 < \delta \le 1\) in \({\mathbb {R}}^{N-1}\) is bounded above and below by a constant times \(\delta ^{\alpha (p.N)}\). We provide explicit estimates for the exponent \(\alpha (p,N)\).


p-Laplacian p-Harmonic measure Shooting method 

Mathematics Subject Classification

34B40 34C11 35J60 



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© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Departament de MatemàtiquesUniversitat Autònoma de BarcelonaBellaterra, BarcelonaSpain
  2. 2.Department of MathematicsUniversity of PittsburghPittsburghUSA
  3. 3.Department of MathematicsUniversity of Illinois at Urbana-ChampaignUrbanaUSA

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