Identification of nonlinearity in conductivity equation via   Dirichlet-to-Neumann map
  We prove that the linear term and quadratic nonlinear term entering a nonlinear elliptic equation of divergence type can be uniquely identified by the Dirichlet to Neuman map. The unique identifiability is proved using the complex geometrical optics solutions and singular solutions. 
Hyeonbae Kang and Gen Nakamura