An inverse problem for the Riemannian minimal surface equation

Cătălin I. Cârstea; Matti Lassas; Tony Liimatainen; Lauri Oksanen

doi:10.1016/j.jde.2023.10.039

An inverse problem for the Riemannian minimal surface equation

Cătălin I. Cârstea^*
, Matti Lassas
, Tony Liimatainen
, Lauri Oksanen

^*此作品的通信作者

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研究成果: Article › 同行評審

6 引文斯高帕斯（Scopus）

摘要

In this paper we consider determining a minimal surface embedded in a Riemannian manifold Σ×R. We show that if Σ is a two dimensional Riemannian manifold with boundary, then the knowledge of the associated Dirichlet-to-Neumann map for the minimal surface equation determine Σ up to an isometry.

原文	English
頁（從 - 到）	626-648
頁數	23
期刊	Journal of Differential Equations
卷	379
DOIs	https://doi.org/10.1016/j.jde.2023.10.039
出版狀態	Published - 15 1月 2024

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10.1016/j.jde.2023.10.039

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title = "An inverse problem for the Riemannian minimal surface equation",

abstract = "In this paper we consider determining a minimal surface embedded in a Riemannian manifold Σ×R. We show that if Σ is a two dimensional Riemannian manifold with boundary, then the knowledge of the associated Dirichlet-to-Neumann map for the minimal surface equation determine Σ up to an isometry.",

keywords = "Higher order linearization, Inverse problems, Minimal surface, Quasilinear elliptic equation, Riemannian manifold, Riemannian surface",

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AU - Cârstea, Cătălin I.

AU - Lassas, Matti

AU - Liimatainen, Tony

AU - Oksanen, Lauri

PY - 2024/1/15

Y1 - 2024/1/15

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AB - In this paper we consider determining a minimal surface embedded in a Riemannian manifold Σ×R. We show that if Σ is a two dimensional Riemannian manifold with boundary, then the knowledge of the associated Dirichlet-to-Neumann map for the minimal surface equation determine Σ up to an isometry.

KW - Higher order linearization

KW - Inverse problems

KW - Minimal surface

KW - Quasilinear elliptic equation

KW - Riemannian manifold

KW - Riemannian surface

UR - https://www.scopus.com/pages/publications/85175462858

U2 - 10.1016/j.jde.2023.10.039

DO - 10.1016/j.jde.2023.10.039

M3 - Article

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SN - 0022-0396

VL - 379

SP - 626

EP - 648

JO - Journal of Differential Equations

JF - Journal of Differential Equations

ER -

An inverse problem for the Riemannian minimal surface equation

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