Optimal size estimates for the inverse conductivity problem with one measurement

被引：59

作者：

Alessandrini, G ^{[1
]}

Rosset, E

Seo, JK

机构：

[1] Univ Trieste, Dipartimento Sci Matemat, I-34100 Trieste, Italy

[2] Yonsei Univ, Dept Math, Seoul 120749, South Korea

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2000年 / 128卷 / 01期

关键词：

inverse conductivity problem; size estimates; Muckenhoupt weights;

D O I：

10.1090/S0002-9939-99-05474-X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove upper and lower estimates on the measure of an inclusion D in a conductor Omega in terms of one pair of current and potential boundary measurements. The growth rates of such estimates are essentially best possible.

引用

页码：53 / 64

页数：12

共 21 条

[11] ON THE UNIQUENESS IN THE INVERSE CONDUCTIVITY PROBLEM WITH ONE MEASUREMENT [J].

FRIEDMAN, A ;

ISAKOV, V .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1989, 38 (03) :563-579

[12] DETECTION OF MINES BY ELECTRIC MEASUREMENTS [J].

FRIEDMAN, A .

SIAM JOURNAL ON APPLIED MATHEMATICS, 1987, 47 (01) :201-212

[13] MONOTONICITY PROPERTIES OF VARIATIONAL INTEGRALS, AP WEIGHTS AND UNIQUE CONTINUATION [J].

GAROFALO, N ;

LIN, FH .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1986, 35 (02) :245-268

[14]

Grisvard P., 1985, MONOGRAPHS STUDIES M, V24

[15] ON THE INVERSE CONDUCTIVITY PROBLEM WITH ONE MEASUREMENT [J].

ISAKOV, V ;

POWELL, J .

INVERSE PROBLEMS, 1990, 6 (02) :311-318

[16] The inverse conductivity problem with one measurement: Stability and estimation of size [J].

Kang, HB ;

Seo, JK ;

Sheen, DW .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1997, 28 (06) :1389-1405

[17] THE NEUMANN PROBLEM FOR ELLIPTIC-EQUATIONS WITH NONSMOOTH COEFFICIENTS [J].

KENIG, CE ;

PIPHER, J .

INVENTIONES MATHEMATICAE, 1993, 113 (03) :447-509

[18]

Kenig CE., 1994, Harmonic Analysis Techniques for Second Order Elliptic Boundary Value Problems

[19]

Lions J-L., 1972, NONHOMOGENEOUS BOUND

[20] ON A SMALL PERTURBATION IN THE 2-DIMENSIONAL INVERSE CONDUCTIVITY PROBLEM [J].

POWELL, J .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1993, 175 (01) :292-304

← 1 2 3 →