On the Perron solution of the caloric Dirichlet problem: an elementary approach

Abstract

By an easy trick taken from caloric polynomial theory, we construct a family \({\mathscr {B}}\) of almost regular domains for the caloric Dirichlet problem. \({\mathscr {B}}\) is a basis of the Euclidean topology. This allows to build, with a basically elementary procedure, the Perron solution to the caloric Dirichlet problem on every bounded domain.