Inverse parabolic problems of determining functions with one spatial-component independence by Carleman estimate

For a parabolic equation in the spatial variable x = (x(1), . . . , x(n) ) and time t, we consider an inverse problem of determining a coefficient which is independent of one spatial component x(n) by lateral boundary data. We apply a Carleman estimate to prove a conditional stability estimate for the inverse problem. Also, we prove similar results for the corresponding inverse source problem.