MOMENTUM RAY TRANSFORMS AND A PARTIAL DATA INVERSE PROBLEM FOR A POLYHARMONIC OPERATOR

被引：6

作者：

Bhattacharyya, Sombuddha ^{[1
]}

Krishnan, Venkateswaran P. ^{[2
]}

Sahoo, Suman K. ^{[3
]}

机构：

[1] Indian Inst Sci Educ & Res, Dept Math, Bhopal, India

[2] TIFR Ctr Applicable Math, Bangalore, Karnataka, India

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

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2023年 / 55卷 / 04期

基金：

欧洲研究理事会;

关键词：

Calderon problem; perturbed polyharmonic operator; tensor tomography; momen-tum ray transforms; BOUNDARY-VALUE PROBLEM; GLOBAL UNIQUENESS; CALDERON PROBLEM; TENSOR-FIELDS; PERTURBATION;

D O I：

10.1137/22M1500617

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study an inverse problem involving the unique recovery of lower order anisotropic tensor perturbations of a polyharmonic operator in a bounded domain from the knowledge of the Dirichlet to Neumann map on a part of a boundary. The uniqueness proof relies on the inversion of generalized momentum ray transforms (MRT) for symmetric tensor fields, which we introduce for the first time to study Calderon-type inverse problems. The uniqueness result and the inversion formula we prove for generalized MRT could be of independent interest and we expect it to be applicable to other inverse problems for higher order operators involving tensor perturbations.

引用

页码：4000 / 4038

页数：39

共 30 条

[21]

Krupchyk K, 2014, T AM MATH SOC, V366, P95

[22] Determining a first order perturbation of the biharmonic operator by partial boundary measurements [J].