报告题目： Heat kernels for non-symmetric diffusions operators with jumps

报告人：张希承  武汉大学

报告时间：12月28日  16:00-17:00

地点：1418

摘要： For $d/geq 2$, we prove the existence and uniqueness of heat kernels to the following time-dependent second order diffusion operator with jumps:$${/cal  L}_t:=/frac{1}{2}/sum_{i,j=1}^da_{ij}(t,x)/partial^2_{ij}+/sum_{i=1}^{d}b_i(t,x)/partial_i +{/cal L}^/kappa_t,$$ where $a=(a_{ij})$ is a uniformly bounded, elliptic, and H/"older continuous matrix-valued function, $b$ belongs to some suitable Kato's class,and ${/cal L}^/kappa_t$ is a non-local $/alpha$-stable-type operatorwith bounded kernel $/kappa$. Moreover, we establish sharp two-sided estimates, gradient estimate and fractional derivative estimate for the heat kernel under some mild conditions.
This is a joint work with Zhen-Qing Chen, Eryan Hu and Longjie Xie