Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4591473 | Journal of Functional Analysis | 2012 | 34 Pages |
Abstract
We consider non-local elliptic operators with kernel K(y)=a(y)/|y|d+σ, where 0<σ<2 is a constant and a is a bounded measurable function. By using a purely analytic method, we prove the continuity of the non-local operator L from the Bessel potential space to Lp, and the unique strong solvability of the corresponding non-local elliptic equations in Lp spaces. As a byproduct, we also obtain interior Lp-estimates. The novelty of our results is that the function a is not necessarily to be homogeneous, regular, or symmetric. An application of our result is the uniqueness for the martingale problem associated to the operator L.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory