Article ID Journal Published Year Pages File Type
4592179 Journal of Functional Analysis 2009 24 Pages PDF
Abstract

It is shown that the second term in the asymptotic expansion as t→0 of the trace of the semigroup of symmetric stable processes (fractional powers of the Laplacian) of order α, for any 0<α<2, in Lipschitz domains is given by the surface area of the boundary of the domain. This brings the asymptotics for the trace of stable processes in domains of Euclidean space on par with those of Brownian motion (the Laplacian), as far as boundary smoothness is concerned.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory