The framework of this paper is given by the mixed boundary‐value problem
$\[\left\{\begin{array}{@{}l@{\quad}l}\Delta u(x)=0,&x;\in \Omega,\\u(x)=0,&x;\in \Gamma _{0},\\\frac{\partial u}{\partial n}(x)=q(x),&x;\in \Gamma _{1},\end{array}\right.\]$
where Ω is a plane domain bounded by a regular curve composed by two arcs Γ0 and Γ1. Assuming that |Γ1|=ε and denoting by u[ε] the solution to this problem, we study some asymptotic expansions in terms of ε which are related to u[ε]. Some connections are presented among these expansions, on one hand, and the geometry of the domain Ω, on the other. In addition, a systematic way is found for computing at the boundary the Ghizzetti's integral that solves the problem.
