CONTRACTIVITY PROPERTIES OF SCHRODINGER SEMIGROUPS ON BOUNDED DOMAINS

We study intrinsic ultracontractivity (IUC) for the Schrodinger operat or H = Delta + V with Dirichlet boundary conditions on bounded domains Omega in R(n). The potential is not assumed either to belong to the K ato class, or to be relatively form-bounded with respect to the Dirich let Laplacian on Omega. The class of domains considered includes John domains and a class of Holder domains. We also give an example of a bo unded domain Omega on which the Dirichlet Laplacian is not IUC, but on which -Delta + V is IUC for a suitable potential V.