Contractivity Properties of Schrödinger Semigroups on Bounded Domains
Fabio Cipriani, Gabriele Grillo · Journal of the London Mathematical Society · 1995
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.