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 $\mathcal{B}$ of $almostregular$ domains for the caloric Dirichlet problem. $\mathcal{B}$ 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.