The determination of a coefficient in an elliptic equation from average flux data

We consider the question of recovering the coefficient q from the equation -Delta u(j) + q(x)u(j) = f(j)(x) subject to homogeneous Dirichlet boundary conditions in a bounded domain Omega subset of R(2). The nonhomogeneous source terms {f(j)(x)}(infinity)(j=1) form a basis for L(2)(Omega). It will be proven that a unique determination is possible from data measurements consisting of measurements of the net flux {integral(Gamma)partial derivative u(j)/partial derivative vds}(infinity)(1) leaving a subset Gamma of the boundary partial derivative Omega for each input source f(j). A continuous dependence result and an algorithm that allows efficient numerical reconstruction of q(x) from finite data is presented.