In this paper, we prove an optimal three-ball inequality for bi-Laplace
equation in some open, connected set. The derivation of such estimate
relies on a delicate Carleman estimate for the bi-Laplace equation and
some Caccioppoli inequalities to estimate the lower-ters. Based on three
-ball inequality, we then derive the vanishing order of solutions, which
is a quantitative version of the strong unique continuation property.