Stability result for elliptic inverse periodic coefficient problem by partial Dirichlet-to-Neumann map

被引：6

作者：

Choulli, Mourad ^{[1
]}

Kian, Yavar ^{[2
]}

Soccorsi, Eric ^{[2
]}

机构：

[1] Univ Lorraine, Inst Elie Cartan Lorraine, CNRS, UMR 7502, Blvd Aiguillettes,BP 70239, F-54506 Vandoeuvre Les Nancy, France

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

来源：

JOURNAL OF SPECTRAL THEORY | 2018年 / 8卷 / 02期

关键词：

Elliptic equation; periodic scalar potential; infinite cylindrical waveguide; stability inequality; partial data; Carleman estimate; BOUNDARY-VALUE PROBLEM; CALDERON PROBLEM; STABLE DETERMINATION; CONDUCTIVITY PROBLEM; CAUCHY DATA; UNIQUENESS;

D O I：

10.4171/JST/212

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the inverse problem of identifying a periodic potential perturbation of the Dirichlet Laplacian acting in an infinite cylindrical domain, whose cross section is assumed to be bounded. We prove log-log stable determination of the potential with respect to the partial Dirichlet-to-Neumannmap, where the Neumann data is taken on slightlymore than half of the boundary of the domain.

引用

页码：733 / 768

页数：36

共 39 条

[11] DOUBLE LOGARITHMIC STABILITY IN THE IDENTIFICATION OF A SCALAR POTENTIAL BY A PARTIAL ELLIPTIC DIRICHLET-TO-NEUMANN MAP [J].

Choulli, M. ;

Kian, Y. ;

Soccorsi, E. .

BULLETIN OF THE SOUTH URAL STATE UNIVERSITY SERIES-MATHEMATICAL MODELLING PROGRAMMING & COMPUTER SOFTWARE, 2015, 8 (03) :78-94

[12]

Choulli M., 2009, MATH APPL BERLIN, V65

[13] STABLE DETERMINATION OF TIME-DEPENDENT SCALAR POTENTIAL FROM BOUNDARY MEASUREMENTS IN A PERIODIC QUANTUM WAVEGUIDE [J].

Choulli, Mourad ;

Kian, Yavar ;

Soccorsi, Eric .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2015, 47 (06) :4536-4558

[14] An inverse anisotropic conductivity problem induced by twisting a homogeneous cylindrical domain [J].

Choulli, Mourad ;

Soccorsi, Eric .

JOURNAL OF SPECTRAL THEORY, 2015, 5 (02) :295-329

[15]

DIXMIER J., 1981, N HOLLAND MATH LIB, V27

[16] UNIQUENESS IN CALDERON'S PROBLEM WITH LIPSCHITZ CONDUCTIVITIES [J].

Haberman, Boaz ;

Tataru, Daniel .

DUKE MATHEMATICAL JOURNAL, 2013, 162 (03) :497-516

[17] A periodic Faddeev-type solution operator [J].

Hahner, P .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1996, 128 (01) :300-308

[18] Stability estimates for the inverse boundary value problem by partial Cauchy data [J].

Heck, Horst ;

Wang, Jenn-Nan .

INVERSE PROBLEMS, 2006, 22 (05) :1787-1796

[19] Inverse conductivity problem in the infinite slab [J].

Ikehata, M .

INVERSE PROBLEMS, 2001, 17 (03) :437-454

[20] Partial Cauchy Data for General Second Order Elliptic Operators in Two Dimensions [J].

Imanuvilov, Oleg Yu ;

Uhlmann, Gunther ;

Yamamoto, Masahiro .

PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES, 2012, 48 (04) :971-1055

← 1 2 3 4 →