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Contractivity Properties of Schrödinger Semigroups on Bounded Domains
Author(s) -
Cipriani Fabio,
Grillo Gabriele
Publication year - 1995
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/52.3.583
Subject(s) - bounded function , laplace operator , class (philosophy) , dirichlet distribution , operator (biology) , domain (mathematical analysis) , mathematics , boundary (topology) , pure mathematics , dirichlet boundary condition , boundary value problem , mathematical analysis , computer science , chemistry , artificial intelligence , biochemistry , repressor , transcription factor , gene
We study intrinsic ultracontractivity (IUC) for the Schrödinger operator H = −Δ + V with Dirichlet boundary conditions on bounded domains Ω in R n . 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 .