2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/224378We consider the inhomogeneous Dirichlet problem on product domains. The main result is the asymptotic expansion of the solution in terms of increasing smoothness up to the boundary. In particular, we show the exact nature of the singularities of the solution at singularities of the boundary by constructing singular functions which make up an asymptotic expansion of the solution.12 pagesAnalysis of PDEs35B65; 35G15text