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

For a parabolic equation in the spatial variable x=(x1,..,xn) and time t, we consider an inverse problem of determining a coefficient which is independent of one spatial component xn 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. © 2021 Walter de Gruyter GmbH, Berlin/Boston 2021.