  In this paper we prove a general uniqueness result in the inverse boundary
value problem for the weighted p-Laplace equation in the plane, with smooth
weights. We also prove a uniqueness result in dimension 3 and higher, for real
analytic weights that are subject to a smallness condition on one of their
directional derivatives. Both results are obtained by linearizing the equation
at a solution without critical points. This unknown solution is then recovered,
together with the unknown weight.
