The regularization B-spline wavelet method for the inverse boundary problem of the Laplace equation from noisy data in an irregular domain

2021 ◽  
Vol 125 ◽  
pp. 1-11
Author(s):  
Xinming Zhang ◽  
Wenxuan Zeng
Keyword(s):  
Boundary Problem ◽  
Laplace Equation ◽  
Noisy Data ◽  
Irregular Domain ◽  
Wavelet Method ◽  
Inverse Boundary ◽  
Spline Wavelet ◽  
B Spline ◽  
Inverse Boundary Problem

scholarly journals On an inverse boundary problem arising in brain imaging

2019 ◽  
Vol 267 (4) ◽  
pp. 2471-2502 ◽  
Author(s):  
Youjun Deng ◽  
Hongyu Liu ◽  
Gunther Uhlmann
Keyword(s):  
Brain Imaging ◽  
Boundary Problem ◽  
Inverse Boundary ◽  
Inverse Boundary Problem

An inverse boundary problem for fourth-order Schrödinger equations with partial data

2019 ◽  
Vol 69 (1) ◽  
pp. 125-138
Author(s):  
Zhiwen Duan ◽  
Shuxia Han
Keyword(s):  
Boundary Problem ◽  
Fourth Order ◽  
Schrodinger Equation ◽  
Geometrical Optics ◽  
Cauchy Data ◽  
Carleman Estimates ◽  
Schrödinger Equations ◽  
Inverse Boundary ◽  
Partial Data ◽  
Inverse Boundary Problem

Abstract In this paper, we show that in dimension n ≥ 3, the knowledge of the Cauchy data for the fourth-order Schrödinger equation measured on possibly very small subsets of the boundary determines uniquely the potential. The proof is based on the Carleman estimates and the construction of complex geometrical optics solutions.

The inverse boundary problem for the Rayleigh system

1995 ◽  
Vol 36 (12) ◽  
pp. 6688-6708 ◽  
Author(s):  
Richard Beals ◽  
G. M. Henkin ◽  
N. N. Novikova
Keyword(s):  
Boundary Problem ◽  
Inverse Boundary ◽  
Inverse Boundary Problem ◽  
Rayleigh System

scholarly journals Boundary regularity for the Ricci equation, geometric convergence, and Gel?fand?s inverse boundary problem

2004 ◽  
Vol 158 (2) ◽  
pp. 261-321 ◽  
Author(s):  
Michael Anderson ◽  
Atsushi Katsuda ◽  
Yaroslav Kurylev ◽  
Matti Lassas ◽  
Michael Taylor
Keyword(s):  
Boundary Problem ◽  
Boundary Regularity ◽  
Inverse Boundary ◽  
Geometric Convergence ◽  
Inverse Boundary Problem
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