We give an L2-well posedness result concerning an initial boundary value problem
for the system of linear elasticity either in the half-plane or in a two dimensional bounded domain.
Under the necessary uniform Kreiss Lopatinskii condition we construct here a dissipative Kreiss
symmetrizer of our problem; actually, due to the characteristic boundary and the lack of a technical
assumption given by T. Ohkubo, the main difficulty consists of building the dissipative symmetrizer
near some special "boundary points".