Comportement des noyaux de la chaleur des opérateurs de Schrödinger et applications à certaines équations paraboliques semi-linéaires

We consider general Schrödinger operators on domains of Riemannian manifolds with possibly exponential volume growth. We prove sharp large time Gaussian upper bounds. These bounds are then used to prove new Lp–Lp estimates for the corresponding semigroups. Applications to semi-linear parabolic equations are given. © 2006 Elsevier Inc. All rights reserved.