Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5773995 | Journal of Differential Equations | 2017 | 59 Pages |
Abstract
For d⩾2, we prove the existence and uniqueness of heat kernels to the following time-dependent second order diffusion operator with jumps:Lt:=12âi,j=1daij(t,x)âij2+âi=1dbi(t,x)âi+Ltκ, where a=(aij) is a uniformly bounded, elliptic, and Hölder continuous matrix-valued function, b belongs to some suitable Kato's class, and Ltκ is a non-local α-stable-type operator with bounded kernel κ. Moreover, we establish sharp two-sided estimates, gradient estimate and fractional derivative estimate for the heat kernel under some mild conditions.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Zhen-Qing Chen, Eryan Hu, Longjie Xie, Xicheng Zhang,