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Approximate factorizations for non-symmetric jump processes
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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 $\alpha$-stable processes in $C^{1, {\rm Dini}}$ open sets for all $\alpha\in (0, 2)$ and of censored $\alpha$-stable processes in $C^{1, {\rm Dini}}$ open sets for all $\alpha\in (1, 2)$.
Forward citations
Cited by 2 Pith papers
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Capacitary estimates for solutions to nonlocal Dirichlet problems
For nonlocal p-Laplace type equations with measurable coefficients, boundary Hölder regularity holds exactly when the exterior capacity density condition holds, with a quantitative modulus estimate.
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Heat kernel estimates for Markov processes with blowing-up jump kernels
Sharp two-sided heat-kernel estimates are established for symmetric jump Markov processes with jump kernels that blow up at the boundary of a κ-fat domain, under a strict bound on the blow-up's Matuszewska index.
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