P. Kim

collaborators

6 papers

math.PR2026

Heat kernel estimates for Markov processes with blowing-up jump kernels

Soobin Cho, Panki Kim, Renming Song +1

In this paper, we establish sharp two-sided heat kernel estimates for a large class of purely discontinuous symmetric Markov processes on closed subsets $F$ of $R^{d}$ , whos…

math.PR2025

Heat kernel estimates for Markov processes in bounded sets with jump kernels decaying at the boundary

Soobin Cho, Panki Kim, Renming Song +1

In this paper, we study two types of purely discontinuous symmetric Markov processes $X$ in bounded smooth subsets of $R^{d}$ : conservative processes and processes killed eit…

math.PR2025

Heat kernel estimates for Dirichlet forms degenerate at the boundary

Soobin Cho, Panki Kim, Renming Song +1

The goal of this paper is to establish sharp two-sided estimates on the heat kernels of two types of purely discontinuous symmetric Markov processes in the upper half-space of $\ma…

math.PR2025

Potential theory of Dirichlet forms with jump kernels blowing up at the boundary

Panki Kim, Renming Song, Zoran VondraÄek

In this paper we study the potential theory of Dirichlet forms on the half-space $R_{+}^{d}$ defined by the jump kernel $J (x, y) = ∣ x - y ∣^{- d - I^\pm} B (x, y)$ and the killing…

math.PR2025

Stability of HÃ¶lder regularity and weighted functional inequalities

Soobin Cho, Panki Kim

We study symmetric Dirichlet forms on metric measure spaces, which may possess both strongly local and pure-jump parts. We introduce a new formulation of a tail condition for jump…

math.PR2025

Heat kernel estimates for SchrÃ¶dinger operators with supercritical killing potentials

Soobin Cho, Panki Kim, Renming Song

In this paper, we study the SchrÃ¶dinger operator $I^ - V$ , where $V$ is a supercritical non-negative potential belonging to a large class of functions containing functions of the fo…