Uniqueness for an inverse problem originating from magnetohydrodynamics. A class of smooth domains

We consider the homogeneous Dirichlet problem Δu = - f(u) ≤ 0 in Ω with u = 0 on ∂Ω. We are interested in the inverse problem of determining the nonlinear source f from knowledge of the normal derivative of u, ∂u/∂n, on an open arc Γ of ∂Ω. It is well known that this fails if Ω is a ball. On the other hand, Beretta and Vogelius proved that an analytic source f is uniquely determined from knowledge of (∂u/∂n)Γ if Γ has at least a true corner. In this paper we try to bridge the gap finding a class of smooth domains for which the determination of analytic f is possible.