2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/165261We investigate the Dirichlet solution for a semianalytic continuous function on the boundary of a semianalytic bounded domain in the plane. We show that the germ of the Dirichlet solution at a boundary point with angle greater than 0 lies in a certain quasianalytic class used by Ilyashenko in his work on Hilbert's 16th problem. With this result we can prove that the Dirichlet solution is definable in an o-minimal structure if the angle at a singular boundary point of the domain is an irrational multiple of $π$.37 pagesLogic03C64; 32B20; 35C20; 35J25; 30E15; 30D60; 30D05; 37E35text