On the uniqueness of solution Cauchy's inverse problem for the equation △u = au + b

摘要

The inverse Cauchy problem △u(x) = au(x) + b≥ 0 for x ∈ w, and u = 0, au/av= Φ on γ is shown as having a unique solution within a wide class of simply connected domains w∈R～2 with smooth boundary 7. Here a and b are real numbers to be determined, and Φ is a given function which is normalized by the condition f_γ Φ ds = 1.