Differentiation of Singular Integrals with Piecewise-Continuous Density and Boundary Values of Derivatives of a Cauchy-Type Integral

2005 ◽  
Vol 57 (2) ◽  
pp. 261-270
Author(s):  
S. A. Plaksa
Keyword(s):  
Singular Integrals ◽  
Cauchy Type ◽  
Boundary Values ◽  
Cauchy Type Integral ◽  
Continuous Density ◽  
Type Integral ◽  
Piecewise Continuous ◽  
Derivatives Of

On estimate for the modulus of continuity of the Cauchy-type integral having a Lipschitz-continuous density

2013 ◽  
Vol 63 (1) ◽  
Author(s):  
Jaroslav Drobek
Keyword(s):  
Modulus Of Continuity ◽  
Cauchy Type ◽  
Regular Boundary ◽  
Boundary Values ◽  
Cauchy Type Integral ◽  
Lipschitz Continuous ◽  
Continuous Density ◽  
Jordan Region ◽  
Type Integral ◽  
Parameter Dependent

AbstractThe Cauchy-type integral having a Lipschitz-continuous density is under investigation. It is considered in a Jordan region that has a piecewise regular boundary without cusps and therefore it can be continuously extended over the closure of the region. Then the boundary values form a function, whose modulus of continuity is to be estimated. One parameter-dependent estimate is obtained and one algorithm for its evaluating is developed. The algorithm is demonstrated on some examples.

scholarly journals A property of the β-Cauchy-type integral with continuous density

2008 ◽  
Vol 60 (11) ◽  
pp. 1683-1690 ◽  
Author(s):  
R. Abreu Blaya ◽  
J. Bory Reyes
Keyword(s):  
Cauchy Type ◽  
Cauchy Type Integral ◽  
Continuous Density ◽  
Type Integral

A cauchy-type integral equation arising in potential theory†

1974 ◽  
Vol 4 (1) ◽  
pp. 1-8 ◽  
Author(s):  
M. Lowengrub ◽  
R. P. Srivastav
Keyword(s):  
Integral Equation ◽  
Potential Theory ◽  
Cauchy Type ◽  
Cauchy Type Integral ◽  
Type Integral
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