  We consider the inverse problem of finding unknown elastic parameters from
internal measurements of displacement fields for tissues. The measurements are
made on the entirety of a smooth domain. Since tissues can be modeled as
quasi-incompressible fluids, we examine the Stokes system and consider only the
recovery of shear modulus distributions. Our main result is to establish
Lipschitz stable estimates on the shear modulus distributions from internal
measurements of displacement fields. These estimates imply convergence of a
numerical scheme known as the Landweber iteration scheme for reconstructing the
shear modulus distributions.
