Inverse coefficient problems for a transport equation by local Carleman estimate

We consider the transport equation partial derivative(t)u(x, t) + (H(x) . del u(x, t)) + p(x)u(x, t) = 0 in Omega x (0, T) where Omega subset of R-n is a bounded domain, and discuss two inverse problems which consist of determining a vector-valued function H(x) or a real-valued function p(x) by initial values and data on a subboundary of Omega. Our results are conditional stability of Holder type in a subdomain D provided that the outward normal component of H(x) is positive on partial derivative D boolean AND partial derivative Omega. The proofs are based on a Carleman estimate where the weight function depends on H.