scholarly journals The Poisson problem for the fractional Hardy operator: Distributional identities and singular solutions

2021 ◽  
pp. 1
Author(s):  
Huyuan Chen ◽  
Tobias Weth
Keyword(s):  
Hardy Operator ◽  
Singular Solutions ◽  
Poisson Problem

Finite Element Method for Solving Problems with Singular Solutions.

1995 ◽  
Author(s):  
I. Babuska ◽  
B. Andersson ◽  
B. Guo ◽  
H. S. Oh ◽  
J. M. Melenk
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Singular Solutions ◽  
Element Method

scholarly journals Singular solutions in soft limits

2020 ◽  
Vol 2020 (5) ◽  
Author(s):  
Freddy Cachazo ◽  
Bruno Umbert ◽  
Yong Zhang
Keyword(s):  
Singular Solutions

scholarly journals Driving forces on dislocations: finite element analysis in the context of the non-singular dislocation theory

2021 ◽  
Author(s):  
Xiandong Zhou ◽  
Christoph Reimuth ◽  
Peter Stein ◽  
Bai-Xiang Xu
Keyword(s):  
Finite Element ◽  
Dislocation Loop ◽  
Driving Force ◽  
Complex Geometry ◽  
Driving Forces ◽  
Singular Solutions ◽  
Dislocation Model ◽  
Configurational Force ◽  
Element Analysis ◽  
Dislocation Configuration

AbstractThis work presents a regularized eigenstrain formulation around the slip plane of dislocations and the resultant non-singular solutions for various dislocation configurations. Moreover, we derive the generalized Eshelby stress tensor of the configurational force theory in the context of the proposed dislocation model. Based on the non-singular finite element solutions and the generalized configurational force formulation, we calculate the driving force on dislocations of various configurations, including single edge/screw dislocation, dislocation loop, interaction between a vacancy dislocation loop and an edge dislocation, as well as a dislocation cluster. The non-singular solutions and the driving force results are well benchmarked for different cases. The proposed formulation and the numerical scheme can be applied to any general dislocation configuration with complex geometry and loading conditions.

scholarly journals Symmetry and monotonicity of singular solutions of double phase problems

2021 ◽  
Vol 280 ◽  
pp. 435-463
Author(s):  
Stefano Biagi ◽  
Francesco Esposito ◽  
Eugenio Vecchi
Keyword(s):  
Singular Solutions ◽  
Double Phase

scholarly journals On Boundedness of Weighted Hardy Operator in and Regularity Condition

2010 ◽  
Vol 2010 (1) ◽  
pp. 837951 ◽  
Author(s):  
Aziz Harman ◽  
FarmanImran Mamedov
Keyword(s):  
Regularity Condition ◽  
Hardy Operator

Complex and Singular Solutions of KdV and MKdV Equations

1986 ◽  
Vol 34 (6B) ◽  
pp. 729-731 ◽  
Author(s):  
B Buti ◽  
N N Rao ◽  
S B Khadkikar
Keyword(s):  
Singular Solutions
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