  We use the method of higher order linearization to study an inverse boundary
value problem for the minimal surface equation on a Riemannian manifold
$(\mathbb{R}^n,g)$, where the metric $g$ is conformally Euclidean. In
particular we show that with the knowledge of Dirichlet-to-Neumann map
associated to the minimal surface equation, one can determine the Taylor series
of the conformal factor $c(x)$ at $x_n=0$ up to a multiplicative constant. We
show this both in the full data case and in some partial data cases.

Analysis of PDEs