Work

An inverse problem for the minimal surface equation

Year: 2022

Type: article

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 (Rn,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 xn=0 up to a multiplicative constant. We show this both in the full data case and in some partial data cases.

Source: Nonlinear Analysis

DOI: 10.1016/j.na.2022.113163

Author: Janne Nurminen

Institution: University of Jyväskylä

Language: English

Topic: Numerical methods in inverse problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,650

Funder: Academy of Finland