Unique continuation for ? with square-integrable potentials

In this paper, we investigate the unique continuation property for the inequality |partial derivative u| <= V|u| , where u is a vector-valued function from a domain in C-n to C-N, and the potential V is an element of L-2. We show that the strong unique continuation property holds when n = 1, and the weak unique continuation property holds when n >= 2. In both cases, the L-2 integrability condition on the potential is optimal.