Estimates and structure of $\alpha$-harmonic functions

Krzysztof Bogdan; Tadeusz Kulczycki; Mateusz Kwaśnicki

doi:10.1007/s00440-007-0067-0

Estimates and structure of $\alpha$-harmonic functions

概率论 2017-02-15 v2

作者: Krzysztof Bogdan , Tadeusz Kulczycki , Mateusz Kwaśnicki

在 arXiv 上查看 ↗ PDF ↗ DOI ↗

摘要

We prove a uniform boundary Harnack inequality for nonnegative harmonic functions of the fractional Laplacian on arbitrary open set $D$ . This yields a unique representation of such functions as integrals against measures on $D^c\cup \{\infty\}$ satisfying an integrability condition. The corresponding Martin boundary of $D$ is a subset of the Euclidean boundary determined by an integral test.

关键词

harmonic functions harnack inequality fractional laplacian

引用

@article{arxiv.math/0607561,
  title  = {Estimates and structure of $\alpha$-harmonic functions},
  author = {Krzysztof Bogdan and Tadeusz Kulczycki and Mateusz Kwaśnicki},
  journal= {arXiv preprint arXiv:math/0607561},
  year   = {2017}
}

备注

32 pages The original publication in Probability Theory and Related Fields available at www.springerlink.com

Estimates and structure of $\alpha$-harmonic functions

摘要

关键词

引用

备注

相关论文