“Whoa! It's like Spotify but for academic articles.”

Instant Access to Thousands of Journals for just $40/month

Get 2 Weeks Free

Continuity of Harmonic Functions for Non-local Markov Generators



In this paper, we treat a priori estimates of harmonic functions for jump processes associated with non-local operators. Let $\mathcal{L}$ be a non-local operator given by $$\mathcal{L}u(x) = \int_{\mathbb{R}^{d} \backslash \{0\}}(u(x+h)-u(x)-h \cdot \nabla u(x) 1_{\{|h| \leq 1\}}) n(x,h)dh.$$ Under some conditions on n ( x , h ), we prove the Hölder continuity and the uniform continuity of $\mathcal{L}$ -harmonic functions. Our results are extensions of those obtained by Bass and Kassmann (Commun Part Diff Eq 30:1249–1259, 2005 ).



Potential AnalysisSpringer Journals

Published: Jul 1, 2013

DOI: 10.1007/s11118-012-9319-4

Free Preview of First Page

Loading next page...

You're reading a free preview. Subscribe to read the entire article.

And millions more from thousands of peer-reviewed journals, for just $40/month

Get 2 Weeks Free

To be the best researcher, you need access to the best research

  • With DeepDyve, you can stop worrying about how much articles cost, or if it's too much hassle to order — it's all at your fingertips. Your research is important and deserves the top content.
  • Read from thousands of the leading scholarly journals from Springer, Elsevier, Nature, IEEE, Wiley-Blackwell and more.
  • All the latest content is available, no embargo periods.