Monday Analysis Seminar: Heat kernel estimates and parabolic Harnack inequalities for jump processes on metric measure spaces
 Date

2015928 13:30 
2015928 14:30
 Place
 Faculty of Science Buliding #3 Room 210

Speaker/Organizer
 Takashi Kumagai (Kyoto University)

 We consider mixedtype jump processes on metric measure spaces and discuss the stability of twosided heat kernel estimates and parabolic Harnack inequalities. Under the assumption of volume doubling, we establish their equivalent characterizations in terms of the jump kernels and the Poincar\'e inequalities. These are nonlocal versions of the cerebrated work by Grigor'yan and SaloffCoste concerning the stability of parabolic Harnack inequalities. We note that for $\alpha$stablelike processes, our current results are restricted to $\alpha < 2$.
This is a ongoing joint work with Z.Q. Chen (Seattle) and J. Wang (Fuzhou and Kyoto).
Different time. Ancona talks after this lecture.