Abstract

We consider the problem of nonlinear elasticity in two and three dimensions. Under the hypothesis the fluid is incompressible, we recover the displacement field and the Lame parameter from power density measurements in two dimensions. A stability estimate is shown to hold for small displacement fields, under some natural hypotheses on the direction of the displacement, with the background pressure fixed. We also prove in dimensions two and three a stability result for the (nonlinear) Saint-Venant model in the case of displacement solution measurements. The use of over-determined elliptic systems is new in the analysis of non-linear inverse elasticity problems.