Potential Analysis

, Volume 31, Issue 1, pp 57–77 | Cite as

Intrinsic Ultracontractivity for Stable Semigroups on Unbounded Open Sets

Article

Abstract

We study the intrinsic ultracontractivity of the semigroup of the isotropic stable process on an unbounded open set. A two-sided estimate of the first eigenfunction of the semigroup is derived. We obtain general geometric conditions for intrinsic ultracontractivity which yield a necessary and sufficient condition for non-degenerate horn-shaped sets.

Keywords

Intrinsic ultracontractivity Isotropic stable process First eigenfunction 

Mathematics Subject Classifications (2000)

Primary 47D07 60G52 Secondary 60J45 

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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Institute of Mathematics and Computer ScienceWrocław University of TechnologyWrocławPoland

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