Abstract
We study intrinsic ultracontractivity (IUC) for the Schrödinger operator H = −Δ + V with Dirichlet boundary conditions on bounded domains Ω in Rn. The potential is not assumed either to belong to the Kato class, or to be relatively form-bounded with respect to the Dirichlet Laplacian on Ω. The class of domains considered includes John domains and a class of Hölder domains. We also give an example of a bounded domain Ω on which the Dirichlet Laplacian is not IUC, but on which −Δ + V is IUC for a suitable potential V.
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