Dirichlet heat kernel estimates for fractional Laplacian with gradient perturbation

Details Dirichlet heat kernel estimates for fractional Laplacian with gradient perturbation Dirichlet heat kernel estimates for fractional Laplacian with gradient perturbation

2010-11-15

arxiv.org/abs/1011.3273v1

Mathematics

Probability

46 pages

Scientific paper

Suppose $d\geq 2$ and $\alpha \in (1, 2)$. Let $D$ be a bounded $C^{1,1}$ open set in $R^d$ and $b$ an $R^d$-valued function on $R^d$ whose components are in a certain Kato class of the rotationally symmetric $\alpha$-stable process. In this paper, we derive sharp two-sided heat kernel estimates for $\Delta^{\alpha/2}+b\cdot \nabla$ in $D$ with zero exterior condition. We also obtain the boundary Harnack principle for $\Delta^{\alpha/2}+b\cdot \nabla$ in $D$ with explicit decay rate.

Affiliated with

Also associated with

No associations

Rating

Dirichlet heat kernel estimates for fractional Laplacian with gradient perturbation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Dirichlet heat kernel estimates for fractional Laplacian with gradient perturbation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Dirichlet heat kernel estimates for fractional Laplacian with gradient perturbation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-297829