Determining a magnetic Schroedinger operator from partial Cauchy data

被引：104

作者：

Dos Santos Ferreira, David ^{[1
]}

Kenig, Carlos E.

Sjostrand, Johannes

Uhlmann, Gunther

机构：

[1] Univ Paris 13, Inst Galilee, F-93430 Villetaneuse, France

[2] Univ Chicago, Dept Math, Chicago, IL 60637 USA

[3] Ecole Polytech, CMLS, F-91128 Palaiseau, France

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

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2007年 / 271卷 / 02期

关键词：

D O I：

10.1007/s00220-006-0151-9

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this paper we show, in dimension n >= 3, that knowledge of the Cauchy data for the Schrodinger equation in the presence of a magnetic potential, measured on possibly very small subsets of the boundary, determines uniquely the magnetic field and the electric potential. We follow the general strategy of [7] using a richer set of solutions to the Dirichlet problem that has been used in previous works on this problem.

引用

页码：467 / 488

页数：22

共 50 条

[1] Determining a Magnetic Schrödinger Operator from Partial Cauchy Data
David Dos Santos Ferreira
Carlos E. Kenig
Johannes Sjöstrand
Gunther Uhlmann
Communications in Mathematical Physics, 2007, 271 : 467 - 488
[2] Determine a Magnetic Schrodinger Operator with a Bounded Magnetic Potential from Partial Data in a Slab
Liu, Shitao
Yang, Yang
APPLIED MATHEMATICS AND OPTIMIZATION, 2021, 83 (01): : 277 - 296
[3] Recovering a potential from partial Cauchy data
Bukhgeim, AL
Uhlmann, G
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2002, 27 (3-4) : 653 - 668
[4] Determine a Magnetic Schrödinger Operator with a Bounded Magnetic Potential from Partial Data in a Slab
Shitao Liu
Yang Yang
Applied Mathematics & Optimization, 2021, 83 : 277 - 296
[5] STABILITY ESTIMATES FOR A MAGNETIC SCHRODINGER OPERATOR WITH PARTIAL DATA
Potenciano-Machado, Leyter
Ruiz, Alberto
INVERSE PROBLEMS AND IMAGING, 2018, 12 (06) : 1309 - 1342
[6] Determining the temperature from Cauchy data in corner domains
Johansson, B. Tomas
INTERNATIONAL JOURNAL OF COMPUTING SCIENCE AND MATHEMATICS, 2010, 3 (1-2) : 122 - 131
[7] Discrete inverse problems for the Schrodinger operator on the multidimensional square lattice with partial Cauchy data
Horvath, Miklos
Marko, Zoltan
INVERSE PROBLEMS, 2016, 32 (05)
[8] On reconstruction of Lame coefficients from partial Cauchy data
Imanuvilov, Oleg Yu.
Yamamoto, Masahiro
JOURNAL OF INVERSE AND ILL-POSED PROBLEMS, 2011, 19 (06): : 881 - 891
[9] AN INVERSE PROBLEM FOR THE MAGNETIC SCHRODINGER OPERATOR ON RIEMANNIAN MANIFOLDS FROM PARTIAL BOUNDARY DATA
Bhattacharyya, Sombuddha
INVERSE PROBLEMS AND IMAGING, 2018, 12 (03) : 801 - 830
[10] Cauchy problem for partial differential equations with operator coefficients
Fayazov, KS
DOKLADY AKADEMII NAUK, 1996, 348 (05) : 592 - 594

← 1 2 3 4 5 →