Intrinsic Ultracontractivity for Stable Semigroups on Unbounded Open Sets
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- Kwaśnicki, M. Potential Anal (2009) 31: 57. doi:10.1007/s11118-009-9125-9
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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.