Existence and uniqueness results for the Helmholtz equation with second order absorbing boundary conditions

In this Note, we prove the existence and uniqueness of the solution to the Helmholtz equation with second order absorbing boundary conditions in a rec tangle. The problem is completed by appropriate corner conditions. The form al approach makes use of a regularity result for the solution of the homoge neous problem. To this aim, one has to consider explicitly the singularitie s of the Laplacian. (C) Academie des Sciences/Elsevier, Paris.