On the asymptotic expansion of the solution of a DirichletVentcel problem with a small parameter

For the sake of simplicity, we impose the Ventcel condition on one straight line segment G2, denoted by G V and we impose Dirichlet

boundary condition on (our results clearly extend to any partition of G into G V and G D ). The Dirichlet-Ventcel problem is

where small parameter, is the outer normal derivative, and is the tangential derivative.