中科院数学与系统科学研究院
数学研究所
学术报告
非线性分析研讨班
报告人：唐榕 (Johns Hopkins University)
题 目：Nonlocal Filtration Equations on the Heisenberg group
时 间：2022.12.08（星期四）上午09:00-10:00
地 点：腾讯会议: 220-550-093
摘 要：Since the work by Caffarelli-Chan-Silvestre-Vasseur, integro-differential equations naturally arise from models in physics, engineering, and finance, attracting an increasing level of interest. They are also a natural generalization of fractional differential equations. In this talk, we will discuss the nonlocal integro-differential equations on the Heisenberg group. First, we will talk about the motivations to study the nonlocal filtration equations on the Heisenberg group. Then I will establish the existence, uniqueness and some qualitative properties of the solutions. Moreover, we will discuss some regularity results. In particular, the Hölder regularity will hold for the porous medium type equations under consideration.
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