Year: 2025
Type: preprint
Abstract: In this paper, we first extend the approximate factorization for purely discontinuous Markov process established in \cite{CKSV20} by getting rid of some of the conditions imposed in \cite{CKSV20}. Then we apply the approximate factorization to obtain sharp two-sided heat kernel estimates for three classes of processes: stable-like processes with critical killings in $C^{1, {\rm Dini}}$ open sets; killed stable-like processes in the setting of \cite{KW24} in $C^{1, \varepsilon}$ open sets; and non-symmetric stable processes in what we call $C^{1,2{\text - \rm Dini}}$ open sets. In particular, we obtain explicit sharp two-sided heat kernel estimates of killed $α$-stable processes in $C^{1, {\rm Dini}}$ open sets for all $α\in (0, 2)$ and of censored $α$-stable processes in $C^{1, {\rm Dini}}$ open sets for all $α\in (1, 2)$.
Source: arXiv (Cornell University)
Authors: Cho, Soobin, Song, Renming
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6966939997
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