Generation of Analytic Semigroups by Elliptic Operators with DirichletBoundary Conditions in a Cylindrical Domain

We consider an elliptic operator of second order with Dirichlet boundaryconditions in a cylindrical domain. We show that a suitable interpretation of thisoperator in a certain space of continuous functions vanishing on the boundary isthe infinitesimal generator of an analytic semigroup in the space of continuousfunctions. We prove several inclusions of the domain of the infinitesimal generatorand of the real interpolation spaces between this domain and the basic space ofcontinuous functions.