Date | 2024-05-29 |
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Speaker | 조수빈 |

Dept. | University of Illinois Urbana-Champaign |

Room | 선택 |

Time | 16:00-17:00 |

In this presentation, I'll explore the analysis of non-local regular Dirichlet forms on metric measure spaces. Our approach relies on three key assumptions: the presence of a strongly local Dirichlet form with sub-Gaussian heat kernel estimates, a tail estimate governing the jump measure outside balls, and a local energy comparability condition. Our primary objectives include establishing function inequalities such as localized Poincaré, cutoff Sobolev, and Faber-Krahn inequalities, highlighting their inherent stability structures and their implications for the regularity of corresponding harmonic functions. Our results are robust in the sense that the constants in estimates remain bounded, provided that the order of the scale function appearing in the tail estimate and local energy comparability condition, maintains a certain distance from zero.

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