scholarly journals Analytic capacity, rectifiability, and the Cauchy integral

2009 ◽  
pp. 1505-1527 ◽  
Author(s):  
Xavier Tolsa
Keyword(s):  
Analytic Capacity ◽  
Cauchy Integral

The Cauchy Integral, Analytic Capacity, and Uniform Rectifiability

1996 ◽  
Vol 144 (1) ◽  
pp. 127 ◽  
Author(s):  
Pertti Mattila ◽  
Mark S. Melnikov ◽  
Joan Verdera
Keyword(s):  
Analytic Capacity ◽  
Cauchy Integral ◽  
Uniform Rectifiability

Construction of complex potentials for multiply connected domain

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Pyotr N. Ivanshin
Keyword(s):  
Integral Equation ◽  
Analytic Function ◽  
Linear System ◽  
Unbounded Domain ◽  
Connected Domain ◽  
Complex Potential ◽  
Cauchy Integral ◽  
Multiply Connected Domain ◽  
Multiply Connected ◽  
Impermeable Boundary

AbstractThe method of reduction of a Fredholm integral equation to the linear system is generalized to construction of a complex potential – an analytic function in an unbounded multiply connected domain with a simple pole at infinity which maps the domain onto a plane with horizontal slits. We consider a locally sourceless, locally irrotational flow on an arbitrary given 𝑛-connected unbounded domain with impermeable boundary. The complex potential has the form of a Cauchy integral with one linear and 𝑛 logarithmic summands. The method is easily computable.

Sign in / Sign up

Export Citation Format

Share Document