Heat kernel estimates for the Dirichlet fractional Laplacian

  • Zhen-Qing Chen

    University of Washington, Seattle, United States
  • Panki Kim

    Seoul National University, South Korea
  • Renming Song

    University of Illinois at Urbana-Champaign, United States

Abstract

In this paper, we consider the fractional Laplacian on an open subset in with zero exterior condition. We establish sharp two-sided estimates for the heat kernel of such Dirichlet fractional Laplacian in open sets. This heat kernel is also the transition density of a rotationally symmetric -stable process killed upon leaving a open set. Our results are the first sharp two-sided estimates for the Dirichlet heat kernel of a non-local operator on open sets.

Cite this article

Zhen-Qing Chen, Panki Kim, Renming Song, Heat kernel estimates for the Dirichlet fractional Laplacian. J. Eur. Math. Soc. 12 (2010), no. 5, pp. 1307–1329

DOI 10.4171/JEMS/231