104 citations · 233 across the 19 of their papers we have counts for
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Potential theory of Dirichlet forms with jump kernels blowing up at the boundary
Panki Kim, Renming Song, Zoran Vondraček
In this paper we study the potential theory of Dirichlet forms on the half-space defined by the jump kernel and the killing p…
Harnack inequality and interior regularity for Markov processes with degenerate jump kernels
Panki Kim, Renming Song, Zoran Vondraček
In this paper we study interior potential-theoretic properties of purely discontinuous Markov processes in proper open subsets . The jump kernels of the proc…
Potential theory of Dirichlet forms degenerate at the boundary: the case of no killing potential
Panki Kim, Renming Song, Zoran Vondraček
In this paper we consider the Dirichlet form on the half-space defined by the jump kernel , where can be de…
Heat kernel estimates for subordinate Markov processes and their applications
Soobin Cho, Panki Kim, Renming Song +1
In this paper, we establish sharp two-sided estimates for transition densities of a large class of subordinate Markov processes. As applications, we show that the parabolic Harnack…
On potential theory of Markov processes with jump kernels decaying at the boundary
Panki Kim, Renming Song, Zoran Vondraček
Motivated by some recent potential theoretic results on subordinate killed Lévy processes in open subsets of the Euclidean space, we study processes in an open set $D\subset {\math…
On the boundary theory of subordinate killed Lévy processes
Panki Kim, Renming Song, Zoran Vondraček
Let be a subordinate Brownian motion in , , via a subordinator with Laplace exponent . We kill the process upon exiting a bounded open set $D\subs…