On the modulus of continuity of solid derivatives of a Cauchy-type integral

1998 ◽  
Vol 50 (4) ◽  
pp. 539-549 ◽  
Author(s):  
O. F. Gerus
Keyword(s):  
Modulus Of Continuity ◽  
Cauchy Type ◽  
Cauchy Type Integral ◽  
Type Integral ◽  
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.

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