Inverse problems for a fractional conductivity equation

被引：17

作者：

Covi, Giovanni ^{[1
]}

机构：

[1] Univ Jyvaskyla, Dept Math, Jyvaskyla, Finland

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2020年 / 193卷 / 193期

基金：

欧洲研究理事会;

关键词：

Fractional conductivity equation; Non-local operators; Inverse problems; Calderon problem;

D O I：

10.1016/j.na.2019.01.008

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper shows global uniqueness in two inverse problems for a fractional conductivity equation: an unknown conductivity in a bounded domain is uniquely determined by measurements of solutions taken in arbitrary open, possibly disjoint subsets of the exterior. Both the cases of infinitely many measurements and a single measurement are addressed. The results are based on a reduction from the fractional conductivity equation to the fractional Schrodinger equation, and as such represent extensions of previous works. Moreover, a simple application is shown in which the fractional conductivity equation is put into relation with a long jump random walk with weights. (C) 2019 The Author (s). Published by Elsevier Ltd.

引用

页数：18

共 21 条

[1]

[Anonymous], 2017, ARXIV151207379V2

[2]

Bourgain J, 2001, OPTIMAL CONTROL AND PARTIAL DIFFERENTIAL EQUATIONS, P439

[3] Gagliardo-Nirenberg, composition and products in fractional Sobolev spaces [J].