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

Two basic boundary-value problems for the inhomogeneous Cauchy–Riemann equation in an infinite... Abstract. 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Pure and Applied Mathematics de Gruyter

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

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Publisher
de Gruyter
Copyright
Copyright © 2012 by the
ISSN
1867-1152
eISSN
1869-6090
DOI
10.1515/apam-2012-0009
Publisher site
See Article on Publisher Site

Abstract

Abstract. 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.

Journal

Advances in Pure and Applied Mathematicsde Gruyter

Published: Aug 1, 2012

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