A uniqueness theorem for determining conductivity from overspecified boundary data (Q1116384)

The problem considered is to find the unknown coefficient k(u) in the nonlinear elliptic equation \[ \nabla (k(u)\nabla u)=f(x,y)\quad (x,y)\in \Omega \] with some overspecified boundary condition on a part of the boundary of the bounded domain \(\Omega\). The author shows that this inverse problem can be reduced to solving a linear singular integral equation and that under certain conditions the solution is unique.