Inverse Problems for the Monge--Ampère Equation: Linearization and Nonlinear Recovery

Gunther Uhlmann, Philipp Zimmermann

We study inverse boundary value problems for the nonlinear Monge--Ampère equation \[ \det D^2u=a(x,u,\nabla u) \] in a bounded domain. We introduce a nonlinear Cauchy data set and…