An inverse problem for the minimal surface equation. (February 2023)

• Record Type: Journal Article
• Authors: Nurminen, Janne
• Is Part Of: Nonlinear analysis. Volume 227(2023)
• Publication Date: 2023-02
• Subjects: Inverse problem -- Higher order linearization -- Quasilinear elliptic equation -- Minimal surface equation; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2022.113163
• Languages: English
• ISSNs: 0362-546X

Abstract

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.