Tuesday, June 25, 2019 - 10:15 in V4-119
Stability of heat kernel estimates and parabolic Harnack inequalities for symmetric Dirichlet forms
A talk in the Oberseminar Geometric Analysis series by
Takashi Kumagai from Kyoto
| Abstract: |
We consider symmetric Dirichlet forms that consist of strongly local (diffusion) part and non-local (jump) part on a metric measure space. Under general volume doubling condition and some mild assumptions on scaling functions, we establish stability of two-sided heat kernel estimates in terms of Poincar\'e inequalities, jumping kernels and generalized capacity inequalities. We also discuss characterizations of the associated parabolic Harnack inequalities. Our results apply to symmetric diffusions with jumps even when the underlying spaces have walk dimensions larger than 2. This is a joint work with Z.Q. Chen (Seattle) and J. Wang (Fuzhou).
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