Sharp Observability Inequalities for the 1-D Plate Equation with a Potential

This paper deals with the problem of sharp observability inequality for the 1-D plate equation wtt ＋ wxxxx ＋ q（t, x）w = 0 with two types of boundary conditions w = wxx = 0 or w = wx = 0, and q（t, x） being a suitable potential. The author shows that 2 the sharp observability constant is of order exp（C｜｜q｜｜^2/7∞） for ｜｜q｜｜∞〉 1. The main tools to derive the desired observability inequalities are the global Carleman inequalities, based on a new point wise inequality for the fourth order plate operator.