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SUMMARY:Kyung-Youn Kim (National Chung Hsing University)
DTSTART:20231101T060000Z
DTEND:20231101T070000Z
DTSTAMP:20260423T021410Z
UID:MAC8028/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MAC8028/6/">
 Potential theory of anisotropic Markov processes</a>\nby Kyung-Youn Kim (N
 ational Chung Hsing University) as part of Trends in Mathematical Research
 \n\nLecture held in NTNU Gongguan S101.\n\nAbstract\nHeat kernel is the fu
 ndamental solution of the heat equation\, and it is also the transition de
 nsity of the diffusion process corresponding to the Laplacian. These relat
 ion is also ture for non-local operators\, and corresponding process  is a
  discontinuous Markov process. \nIn this talk\, we consider anisotropic Ma
 rkov processes.\nLet $L_i$\, $i=1\,\\ldots\,d$\, be identical and independ
 ent $1$-dimensional L\\'evy processes.\nDefine a Markov process $M:=(M_1\,
  \\ldots\, M_d)$ whose jumping kernel is comparable to that of $L:=(L_1\, 
 \\ldots\, L_d)$.\nThen $M$ is a pure jump process that jumps parallel to t
 he coordinate axes.\nWe discuss the sharp two-sided heat kernel bounds for
  $M$ on $C^{1\,1}$ open set $D\\subset {\\rm I\\!R}^d$ as well as the pote
 ntial theory of anisotropic Markov process. This is the joint work with Li
 dan Wang.\n \n\n\n[1.] Dirichlet Heat kernel estimates for a large class o
 f anisotropic Markov process(with Lidan Wang).\n
LOCATION:https://researchseminars.org/talk/MAC8028/6/
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