Asymptotic expansions for membranes subjected to a lifting force in a part of their boundary

The framework of this paper is given by the mixed boundary-value problem (GRAPHICS) where Omega is a plane domain bounded by a regular curve composed by two arcs Gamma(0) and Gamma(1). Assuming that Gamma(1)=epsilon and denoting by u[epsilon] the solution to this problem, we study some asymptotic expansions in terms of epsilon which are related to u[epsilon]. Some connections are presented among these expansions, on one hand, and the geometry of the domain Omega, on the other. In addition, a systematic way is found for computing at the boundary the Ghizzetti's integral that solves the problem.