TWO BOUNDARY VALUE PROBLEMS OF NONHOMOGENEOUS CAUCHY{RIEMANN EQUATION IN A MINOR SEGMENT OF UNIT DISC

In this article, by the parqueting-reflection method we obtainthe Schwarz{Poisson formula in a minor segment of unit disc. Then weconsider the Schwarz and Dirichlet boundary value problems for the non-homogeneous Cauchy{Riemann equation and expressions of solution andthe condition of solvability are explicitly obtained.

Keywords:

Cauchy-Pompeiu formula , Schwarz problem , Dirichlet problem , Unit disc