The Cauchy problem for Laplace equation on the plane

2006 ◽  
pp. 89-101
Author(s):  
S. I. Kabanikhin ◽  
G. Dairbaeva
Keyword(s):  
Cauchy Problem ◽  
Laplace Equation ◽  
The Cauchy Problem

scholarly journals A modified Tikhonov regularization method based on Hermite expansion for solving the Cauchy problem of the Laplace equation

2020 ◽  
Vol 18 (1) ◽  
pp. 1685-1697
Author(s):  
Zhenyu Zhao ◽  
Lei You ◽  
Zehong Meng
Keyword(s):  
Cauchy Problem ◽  
Laplace Equation ◽  
Tikhonov Regularization ◽  
Regularization Method ◽  
Regularization Parameter ◽  
Solution Process ◽  
Tikhonov Regularization Method ◽  
Hermite Expansion ◽  
The Cauchy Problem ◽  
Ill Posed

Abstract In this paper, a Cauchy problem for the Laplace equation is considered. We develop a modified Tikhonov regularization method based on Hermite expansion to deal with the ill posed-ness of the problem. The regularization parameter is determined by a discrepancy principle. For various smoothness conditions, the solution process of the method is uniform and the convergence rate can be obtained self-adaptively. Numerical tests are also carried out to verify the effectiveness of the method.

On the Cauchy Problem for the Three-Dimensional Laplace Equation

2021 ◽  
Vol 65 (2) ◽  
pp. 49-64
Author(s):  
A. B. Khasanov ◽  
F. R. Tursunov
Keyword(s):  
Cauchy Problem ◽  
Laplace Equation ◽  
Three Dimensional ◽  
The Cauchy Problem

scholarly journals The a posteriori Fourier method for solving the Cauchy problem for the Laplace equation with nonhomogeneous Neumann data

2013 ◽  
Vol 37 (14-15) ◽  
pp. 7764-7777 ◽  
Author(s):  
Chu-Li Fu ◽  
Yun-Jie Ma ◽  
Hao Cheng ◽  
Yuan-Xiang Zhang
Keyword(s):  
Cauchy Problem ◽  
Laplace Equation ◽  
Fourier Method ◽  
A Posteriori ◽  
The Cauchy Problem

Uniqueness and free interpolation for logarithmic potentials and the cauchy problem for the laplace equation in 529-1529-1529-1

1995 ◽  
Vol 5 (3) ◽  
pp. 529-571 ◽  
Author(s):  
A. Aleksandrov ◽  
J. Bourgain ◽  
M. Giesecke ◽  
V. Havin ◽  
Yu Vymenets
Keyword(s):  
Cauchy Problem ◽  
Laplace Equation ◽  
Logarithmic Potentials ◽  
Free Interpolation ◽  
The Cauchy Problem

scholarly journals On a numerical solution of the Cauchy problem for the Laplace equation by the fundamental solutions method

PAMM ◽  
2007 ◽  
Vol 7 (1) ◽  
pp. 2040035-2040036
Author(s):  
Takashi Ohe ◽  
Katsu Yamatani ◽  
Kohzaburo Ohnaka
Keyword(s):  
Cauchy Problem ◽  
Numerical Solution ◽  
Laplace Equation ◽  
Fundamental Solutions ◽  
The Cauchy Problem

Stability results for the Cauchy problem for the Laplace equation in a strip

2003 ◽  
Vol 19 (4) ◽  
pp. 833-844 ◽  
Author(s):  
Dinh Nho H o ◽  
Pham Minh Hien
Keyword(s):  
Cauchy Problem ◽  
Laplace Equation ◽  
The Cauchy Problem ◽  
Stability Results
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