Abstract
In this paper, sharp two-sided estimates for the transition densities of relativistic α-stable processes with mass m∈(0, 1] in C 1,1 exterior open sets are established for all time t>0. These transition densities are also the Dirichlet heat kernels of m-(m 2/α-δ) α/2 with m∈(0, 1] in C 1,1 exterior open sets. The estimates are uniform in m in the sense that the constants are independent of m∈(0, 1]. As a corollary of our main result, we establish sharp two-sided Green function estimates for relativistic α-stable processes with mass m∈(0, 1] in C 1,1 exterior open sets.
| Original language | English |
|---|---|
| Pages (from-to) | 448-475 |
| Number of pages | 28 |
| Journal | Journal of Functional Analysis |
| Volume | 263 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 15 Jul 2012 |
| Externally published | Yes |
Keywords
- Exit time
- Green function
- Heat kernel
- Lévy system
- Parabolic Harnack inequality
- Relativistic stable process
- Symmetric α-stable process
- Transition density
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Chen, Z. Q., Kim, P., & Song, R. (2012). Global heat kernel estimate for relativistic stable processes in exterior open sets. Journal of Functional Analysis, 263(2), 448-475. https://doi.org/10.1016/j.jfa.2012.04.012