Lipschitz stability for a piecewise linear Schrodinger potential from local Cauchy data

We consider the inverse boundary value problem of determining the potential q in the equation Δu+qu=0 in Ω⊂Rn, 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 Ω. No sign, nor spectrum condition on q is assumed, hence our treatment encompasses the reduced wave equation Δu+k2c−2u=0 at fixed frequency k.