scholarly journals The Cauchy problem for a nonlinear elliptic equation: Nash-game approach and application to image inpainting

2015 ◽  
Vol 9 (3) ◽  
pp. 853-874 ◽  
Author(s):  
Anis Theljani ◽  
Maher Moakher ◽  
Moez Kallel
Keyword(s):  
Cauchy Problem ◽  
Elliptic Equation ◽  
Nonlinear Elliptic Equation ◽  
Image Inpainting ◽  
Nash Game ◽  
Nonlinear Elliptic ◽  
The Cauchy Problem

scholarly journals HP estimation for the Cauchy problem for nonlinear elliptic equation

2018 ◽  
Vol 1 (T5) ◽  
pp. 193-202
Author(s):  
Thang Duc Le
Keyword(s):  
Cauchy Problem ◽  
Exact Solution ◽  
Elliptic Equation ◽  
Error Estimates ◽  
Bounded Domain ◽  
Nonlinear Elliptic Equation ◽  
Nonlinear Elliptic ◽  
The Cauchy Problem ◽  
Ill Posed ◽  
Regularized Solution

In this paper, we investigate the Cauchy problem for a ND nonlinear elliptic equation in a bounded domain. As we know, the problem is severely ill-posed. We apply the Fourier truncation method to regularize the problem. Error estimates between the regularized solution and the exact solution are established in Hp space under some priori assumptions on the exact solution.

Nonlinear Elliptic Equations in Strip-Like Domains

2012 ◽  
Vol 12 (4) ◽  
Author(s):  
Jaeyoung Byeon ◽  
Kazunaga Tanaka
Keyword(s):  
Elliptic Equation ◽  
Positive Solution ◽  
Bounded Domain ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equation ◽  
Nonlinear Elliptic Equations ◽  
Nonlinear Elliptic

AbstractWe study the existence of a positive solution of a nonlinear elliptic equationwhere k ≥ 2 and D is a bounded domain domain in R

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