Asymptotic solution of 2D and 3D boundary integral equations arising in Fluid Mechanics and Electrostatics

We present a systematic method to asymptotically expand, with respect to a small slenderness or thickness parameter, the solution of a wide class of b oundary integral equations arising in Electrostatics and Fluid Mechanics. T he adopted point of view permits us to bypass the tedious matching rules of the widely employed method of matched asymptotic expansions. If each step of the proposed procedure is described within a general framework, the pape r also addresses applications to 2D and 3D problems. The 3D example not onl y briefly reports but also extends the results obtained elsewhere by the au thor. The whole 2D application to the potential flow around a thin aifoil i s original. Finally, a special attention is paid to the case of a non-smoot h 2D domain.