Stability of Dirichlet heat kernel estimates for non-local operators under Feynman-Kac perturbation
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- by Zhen-Qing Chen, Panki Kim and Renming Song PDF
- Trans. Amer. Math. Soc. 367 (2015), 5237-5270 Request permission
Abstract:
In this paper we show that Dirichlet heat kernel estimates for a class of (not necessarily symmetric) Markov processes are stable under non-local Feynman-Kac perturbations. This class of processes includes, among others, (reflected) symmetric stable-like processes in closed $d$-sets in $\mathbb {R}^d$, killed symmetric stable processes, censored stable processes in $C^{1, 1}$ open sets, as well as stable processes with drifts in bounded $C^{1, 1}$ open sets. These two-sided estimates are explicit involving distance functions to the boundary.References
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Additional Information
- Zhen-Qing Chen
- Affiliation: Department of Mathematics and Research Institute of Mathematics, University of Washington, Seattle, Washington 98195
- MR Author ID: 242576
- ORCID: 0000-0001-7037-4030
- Email: zqchen@uw.edu
- Panki Kim
- Affiliation: Department of Mathematics, Seoul National University, Building 27, 1 Gwanak-ro, Gwanak-gu, Seoul 151-747, Republic of Korea
- MR Author ID: 705385
- Email: pkim@snu.ac.kr
- Renming Song
- Affiliation: Department of Mathematics, University of Illinois, Urbana, Illinois 61801
- MR Author ID: 229187
- Email: rsong@math.uiuc.edu
- Received by editor(s): May 3, 2012
- Received by editor(s) in revised form: May 7, 2013, and May 17, 2013
- Published electronically: November 10, 2014
- Additional Notes: The research of Zhen-Qing Chen was partially supported by NSF Grants DMS-0906743, DMS-1206276 and DMR-1035196.
The research of Panki Kim was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No.2009-0083521)
The research of Renming Song was supported in part by a grant from the Simons Foundation (208236) - © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 367 (2015), 5237-5270
- MSC (2010): Primary 60J35, 47G20, 60J75; Secondary 47D07, 47D08
- DOI: https://doi.org/10.1090/S0002-9947-2014-06190-4
- MathSciNet review: 3335416