An inverse problem for the Riemannian minimal surface equation

被引：2

作者：

Carstea, Catalin I. ^{[1
]}

Lassas, Matti ^{[2
]}

Liimatainen, Tony ^{[2
]}

Oksanen, Lauri ^{[2
]}

机构：

[1] Natl Yang Ming Chiao Tung Univ, Dept Appl Math, Hsinchu, Taiwan

[2] Univ Helsinki, Dept Math & Stat, Helsinki, Finland

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2024年 / 379卷

基金：

芬兰科学院;

关键词：

Inverse problems; Quasilinear elliptic equation; Riemannian manifold; Riemannian surface; Minimal surface; Higher order linearization; GLOBAL UNIQUENESS; CONDUCTIVITIES;

D O I：

10.1016/j.jde.2023.10.039

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we consider determining a minimal surface embedded in a Riemannian manifold E x R. We show that if E is a two dimensional Riemannian manifold with boundary, then the knowledge of the associated Dirichlet-to-Neumann map for the minimal surface equation determine E up to an isometry. (c) 2023 Elsevier Inc. All rights reserved.

引用

页码：626 / 648

页数：23

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