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

We consider the homogeneous Dirichlet problem Delta u = -f (u) <= 0 in Omega with u = 0 on delta Omega. We are interested in the inverse problem of determining the nonlinear source f from knowledge of the normal derivative of u, partial derivative u/partial derivative n, on an open arc Gamma of partial derivative. It is well known that this fails if Omega is a ball. On the other hand, Beretta and Vogelius proved that an analytic source f is uniquely determined from knowledge of (partial derivative u/partial derivative n)vertical bar Gamma if Gamma 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.