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arXiv · 2203.09272

An inverse problem for the minimal surface equation

Janne Nurminen
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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 $(\mathbb{R}^n,g)$, 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.

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Janne Nurminen. 2022-03-17. An inverse problem for the minimal surface equation. https://doi.org/10.1016/j.na.2022.113163

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