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Licensed Unlicensed Requires Authentication Published by De Gruyter August 1, 2012

Two basic boundary-value problems for the inhomogeneous Cauchy–Riemann equation in an infinite sector

Mohamed S. Akel and Hussein S. Hussein


The object of the present article is to investigate the Schwarz and Dirichlet boundary value problems for the inhomogeneous Cauchy–Riemann equation in an infinite sector. Firstly, we obtain the Schwarz–Poisson formula in a sector with angle (). Secondly, boundary behaviors of some linear integrals will be studied, especially at the corner point. Finally, the solutions and the conditions of solvability are explicitly obtained.

Received: 2011-09-15
Revised: 2012-06-03
Accepted: 2012-06-03
Published Online: 2012-08-01
Published in Print: 2012-08-01

© 2012 by Walter de Gruyter Berlin Boston

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