The inverse conductivity problem with one measurement: Stability and estimation of size

被引:88
作者
Kang, HB
Seo, JK
Sheen, DW
机构
[1] YONSEI UNIV,DEPT MATH,SEOUL 120749,SOUTH KOREA
[2] SEOUL NATL UNIV,DEPT MATH,SEOUL 151742,SOUTH KOREA
关键词
inverse problem; stability;
D O I
10.1137/S0036141096299375
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We consider the inverse problem to the refraction problem div((1+(k-1)X-D)del u) = 0 in Omega and partial derivative u/partial derivative v = g on partial derivative Omega. The inverse problem is to determine the size and the location of an unknown object D from the boundary measurement ho(g) = u/(partial derivative Omega). The results of this paper are twofold: stability and estimation of size of D. We first obtain upper and lower bounds of the size of D by comparing Lambda(D)(g) with the Dirichlet data corresponding to the harmonic equation with the same Neumann data g. We then obtain logarithmic stability in the case of the disks. In the course of deriving the stability, we are able to compute a positive lower bound (independent of D) of the gradient of the solution u to the refraction problem with the Neumann data g satisfying some mild conditions.
引用
收藏
页码:1389 / 1405
页数:17
相关论文
共 14 条
[2]   LOCAL UNIQUENESS IN THE INVERSE CONDUCTIVITY PROBLEM WITH ONE MEASUREMENT [J].
ALESSANDRINI, G ;
ISAKOV, V ;
POWELL, J .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1995, 347 (08) :3031-3041
[3]  
Alessandrini G., 1992, ANN SCUOLA NORM-SCI, V19, P567
[4]   THE INVERSE CONDUCTIVITY PROBLEM WITH ONE MEASUREMENT - UNIQUENESS FOR CONVEX POLYHEDRA [J].
BARCELO, B ;
FABES, E ;
SEO, JK .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1994, 122 (01) :183-189
[5]  
BELLOUT H, 1988, ARCH RATION MECH AN, V101, P143, DOI 10.1007/BF00251458
[6]   STABILITY FOR AN INVERSE PROBLEM IN POTENTIAL-THEORY [J].
BELLOUT, H ;
FRIEDMAN, A ;
ISAKOV, V .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1992, 332 (01) :271-296
[7]   POTENTIAL TECHNIQUES FOR BOUNDARY-VALUE PROBLEMS ON C1-DOMAINS [J].
FABES, EB ;
JODEIT, M ;
RIVIERE, NM .
ACTA MATHEMATICA, 1978, 141 (3-4) :165-186
[8]  
Folland G., 1976, INTRO PARTIAL DIFFER, DOI DOI 10.1515/9780691213033
[9]   IDENTIFICATION OF THE CONDUCTIVITY COEFFICIENT IN AN ELLIPTIC EQUATION [J].
FRIEDMAN, A ;
GUSTAFSSON, B .
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1987, 18 (03) :777-787
[10]  
Friedman A., 1989, INDIANA U MATH J, V38, P553