TY - JOUR
T1 - Conditional stability estimation for an inverse boundary problem with non-smooth boundary in R3
AU - Cheng, J.
AU - Hon, Y. C.
AU - Yamamoto, M.
PY - 2001
Y1 - 2001
N2 - In this paper, we investigate an inverse problem of determining a shape of a part of the boundary of a bounded domain in R3 by a solution to a Cauchy problem of the Laplace equation. Assuming that the unknown part is a Lipschitz continuous surface, we give a logarithmic conditional stability estimate in determining the part of boundary under reasonably a priori information of an unknown part. The keys are the complex extension and estimates for a harmonic measure. © 2001 American Mathematical Society.
AB - In this paper, we investigate an inverse problem of determining a shape of a part of the boundary of a bounded domain in R3 by a solution to a Cauchy problem of the Laplace equation. Assuming that the unknown part is a Lipschitz continuous surface, we give a logarithmic conditional stability estimate in determining the part of boundary under reasonably a priori information of an unknown part. The keys are the complex extension and estimates for a harmonic measure. © 2001 American Mathematical Society.
KW - Conditional stability estimation
KW - Determination of unknown boundary
KW - Non-smooth boundary
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U2 - 10.1090/s0002-9947-01-02758-1
DO - 10.1090/s0002-9947-01-02758-1
M3 - 21_Publication in refereed journal
VL - 353
SP - 4123
EP - 4138
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
SN - 0002-9947
IS - 10
ER -