Abstract
We consider the fractional Laplacian - (-Δ) α/2 on an open subset in ℝ d with zero exterior condition. We establish sharp two-sided estimates for the heat kernel of such a Dirichlet fractional Laplacian in C 1,1, open sets. This heat kernel is also the transition density of a rotationally symmetric α-stable process killed upon leaving a C 1,1, open set. Our results are the first sharp twosided estimates for the Dirichlet heat kernel of a non-local operator on open sets.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1307-1327 |
| Number of pages | 21 |
| Journal | Journal of the European Mathematical Society |
| Volume | 12 |
| Issue number | 5 |
| DOIs | |
| State | Published - 2010 |
Keywords
- Boundary harnack inequality
- Exit time
- Fractional Laplacian
- Green function
- Heat kernel
- Intrinsic ultracontractivity
- Lévy system
- Parabolic harnack inequality
- Symmetric α-stable process
- Transition density
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics