A1 Journal article (refereed)
An inverse problem for the minimal surface equation (2023)

Nurminen, J. (2023). An inverse problem for the minimal surface equation. Nonlinear Analysis : Theory, Methods and Applications, 227, Article 113163. https://doi.org/10.1016/j.na.2022.113163

JYU authors or editors

Publication details

All authors or editors: Nurminen, Janne

Journal or series: Nonlinear Analysis : Theory, Methods and Applications

ISSN: 0362-546X

eISSN: 1873-5215

Publication year: 2023

Volume: 227

Article number: 113163

Publisher: Elsevier

Publication country: United Kingdom

Publication language: English

DOI: https://doi.org/10.1016/j.na.2022.113163

Publication open access: Openly available

Publication channel open access: Partially open access channel

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/83773

Web address where publication is available: https://arxiv.org/abs/2203.09272

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 , where the metric 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 at up to a multiplicative constant. We show this both in the full data case and in some partial data cases.

Keywords: inverse problems; equations; partial differential equations

Free keywords: inverse problem; higher order linearization; quasilinear elliptic equation; minimal surface equation

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Ministry reporting: Yes

VIRTA submission year: 2023

JUFO rating: 1