We consider the inverse boundary value problem of determining the potential q in the equation Delta u qu = 0 in Omega subset of R-n, from local Cauchy data. A result of global Lipschitz stability is obtained in dimension n >= 3 for potentials that are piecewise linear on a given partition of Omega. No sign, nor spectrum condition on q is assumed, hence our treatment encompasses the reduced wave equation Delta u + k(2)c(-2)u = 0 at fixed frequency k.