Potential theory of stable processes on domains

 

Hrvoje Sikic
Department of Mathematics, University of Zagreb

The condition of intrinsic ultracontractivity for semigroups of killed Brownian motion on domains implies that all nonnegative harmonic functions of the subordinate killed
Brownian motion on such a domain are continuous and satisfy Harnack inequality. Furthermore, in this case both the Martin boundary and the minimal Martin boundary
coincide with the Euclidean boundary. If in addition the domain is also bounded Lipschitz, then the boundary Harnack principle holds for positive harmonic functions. The talk will emphasize the background and significance of rather technical notions involved in this study.

March 2, 2005 at 15:40 in FENS G016