On $p$-Harmonic Measures in Half Spaces

J. G. Llorente; J. J. Manfredi; W. C. Troy; J. M. Wu

On $p$-Harmonic Measures in Half Spaces

Analysis of PDEs 2018-07-30 v1

Authors: J. G. Llorente , J. J. Manfredi , W. C. Troy , J. M. Wu

Abstract

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

Keywords

harmonic functions lp spaces and inequalities measure theory

Cite

@article{arxiv.1807.10367,
  title  = {On $p$-Harmonic Measures in Half Spaces},
  author = {J. G. Llorente and J. J. Manfredi and W. C. Troy and J. M. Wu},
  journal= {arXiv preprint arXiv:1807.10367},
  year   = {2018}
}

Comments

24 pages

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