Inverse problems for elliptic equations with power type nonlinearities

被引：75

作者：

Lassas, Matti ^{[1
]}

Liimatainen, Tony ^{[2
]}

Lin, Yi-Hsuan ^{[3
]}

Salo, Mikko ^{[2
]}

机构：

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

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

[3] Natl Chiao Tung Univ, Dept Appl Math, Hsinchu, Taiwan

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2021年 / 145卷

基金：

欧盟地平线“2020”; 欧洲研究理事会; 芬兰科学院;

关键词：

Inverse boundary value problem; Calderon problem; Semilinear equation; Transversally anisotropic; CALDERON PROBLEM; GLOBAL UNIQUENESS;

D O I：

10.1016/j.matpur.2020.11.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce a method for solving Calderon type inverse problems for semilinear equations with power type nonlinearities. The method is based on higher order linearizations, and it allows one to solve inverse problems for certain nonlinear equations in cases where the solution for a corresponding linear equation is not known. Assuming the knowledge of a nonlinear Dirichlet-to-Neumann map, we determine both a potential and a conformal manifold simultaneously in dimension 2, and a potential on transversally anisotropic manifolds in dimensions n >= 3. In the Euclidean case, we show that one can solve the Calderon problem for certain semilinear equations in a surprisingly simple way without using complex geometrical optics solutions. (C) 2020 Elsevier Masson SAS. All rights reserved.

引用

页码：44 / 82

页数：39

共 47 条

[1]

[Anonymous], 2005, Cubo

[2]

[Anonymous], ARXIV14064776

[3] MONOTONICITY AND ENCLOSURE METHODS FOR THE p-LAPLACE EQUATION [J].