Résumé: The aim of this work is to show how the usual Boundary Integral Equation techniques can be extended to deal with harmonic problems with oblique boundary conditions. Based on the Green formula, we express the solution in terms of the boundary data. The essential idea is to apply the Grenn Ostrogradsky theorem to translate the tangential derivative to the fundamental solution. The integral equation of second kind Fredholm type is obtained. By Fredholm’s theorem, the existence and uniqueness of the solution is established.

Résumé: The aim of this work is to show how the usual Boundary Integral Equation techniques can be extended to deal with harmonic problems with oblique boundary conditions. Based on the Green formula, we express the solution in terms of the boundary data. The essential idea is to apply the Grenn Ostrogradsky theorem to translate the tangential derivative to the fundamental solution. The integral equation of second kind Fredholm type is obtained. By Fredholm’s theorem, the existence and uniqueness of the solution is established.