唐榕 ,Johns Hopkins University

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 H?lder regularity will hold for the porous medium type equations under consideration.