An inverse problem for the minimal surface equation. (February 2023) - Nurminen, Janne
Abstract: We use the method of higher order linearization to study an inverse boundary value problem for the minimal surface equation on a Riemannian manifold ( 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.