Partial data inverse problems for quasilinear conductivity equations

被引：16

作者：

Kian, Yavar ^{[1
]}

Krupchyk, Katya ^{[2
]}

Uhlmann, Gunther ^{[3
,4
]}

机构：

[1] Aix Marseille Univ, Univ Toulon, CPT, CNRS, Marseille, France

[2] Univ Calif Irvine, Dept Math, Irvine, CA 92697 USA

[3] Univ Washington, Dept Math, Seattle, WA 98195 USA

[4] Hong Kong Univ Sci & Technol, Inst Adv Study, Kowloon, Hong Kong, Peoples R China

来源：

MATHEMATISCHE ANNALEN | 2023年 / 385卷 / 3-4期

基金：

美国国家科学基金会;

关键词：

BOUNDARY-VALUE PROBLEM; GLOBAL UNIQUENESS; ELLIPTIC-EQUATIONS; CALDERON PROBLEM;

D O I：

10.1007/s00208-022-02367-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that the knowledge of the Dirichlet-to-Neumann maps given on an arbitrary open non-empty portion of the boundary of a smooth domain in R-n , n >= 2, for classes of semilinear and quasilinear conductivity equations, determines the nonlinear conductivities uniquely. The main ingredient in the proof is a certain L-1-density result involving sums of products of gradients of harmonic functions which vanish on a closed proper subset of the boundary.

引用

页码：1611 / 1638

页数：28

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