Boundary Problems for Harmonic Functions and Norm Estimates for Inverses of Singular Integrals in Two Dimensions

2005 ◽  
Vol 26 (7-8) ◽  
pp. 851-878 ◽  
Author(s):  
Irina Mitrea
Keyword(s):  
Harmonic Functions ◽  
Singular Integrals ◽  
Two Dimensions ◽  
Boundary Problems ◽  
Norm Estimates

A criterion on oscillation and variation for the commutators of singular integral operators

2015 ◽  
Vol 27 (1) ◽  
Author(s):  
Feng Liu ◽  
Huoxiong Wu
Keyword(s):  
Singular Integral ◽  
Singular Integrals ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Weighted Norm ◽  
Norm Estimates ◽  
Variation Operators

AbstractThis paper gives a criterion on the weighted norm estimates of the oscillatory and variation operators for the commutators of Calderón–Zygmund singular integrals in dimension 1. As applications, the weighted

scholarly journals Inverse Boundary Problems for Systems in Two Dimensions

2013 ◽  
Vol 14 (6) ◽  
pp. 1551-1571 ◽  
Author(s):  
Pierre Albin ◽  
Colin Guillarmou ◽  
Leo Tzou ◽  
Gunther Uhlmann
Keyword(s):  
Two Dimensions ◽  
Boundary Problems ◽  
Inverse Boundary

Approximation Schemes for Singular Integrals and Their Application to Some Boundary Problems

2004 ◽  
Vol 4 (1) ◽  
pp. 94-104
Author(s):  
Jemal Sanikidze ◽  
Manana Mirianashvili
Keyword(s):  
Dirichlet Problem ◽  
Numerical Solution ◽  
Approximate Calculation ◽  
Singular Integrals ◽  
Approximation Schemes ◽  
Cauchy Kernel ◽  
Boundary Problems ◽  
Computational Schemes

Abstract Certain schemes for approximate calculation of singular integrals with a Cauchy kernel and their application to the numerical solution of the modified Dirichlet problem are offered. Questions of justifying the corresponding computational schemes for domains with Lyapunov boundaries are investigated.

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