2
$\begingroup$

Does the Poisson kernel for fractional Laplacian $(-\Delta)^s$ exist for a smooth bounded domain with two boundaries. If so, is there a upper and lower bound for the Poisson kernel.

Improve this question
$\endgroup$

1 Answer 1

Reset to default
1
$\begingroup$

Sure it does! Estimates of the Poisson kernel (and closely related bounds for the Green function) were studied already in the 90s by two independent groups of people: Bogdan, Byczkowski and Kulczycki, and Chen and Song. You can find the estimate you need in Theorem 1.5 in:

  • Z.-Q. Chen, R. Song, Estimates on Green functions and Poisson kernels for symmetric stable processes. Math Ann 312, 465–501 (1998), DOI:10.1007/s002080050232.
Improve this answer
$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .