Schwarz-type problem of nonhomogeneous Cauchy-Riemann equation on a triangle

We consider the Schwarz-type boundary-value problem (BVP) of the nonhomogeneous Cauchy-Riemann equation on an isosceles orthogonal triangle. By the technique of plane parqueting and the Cauchy-Pompeiu formula on the triangle, the Schwarz-Poisson formula is obtained. We also investigate boundary behaviors of the Schwarz-type operator and the Pompeiu-type operator. Especially, boundary-values at the corners are proved to exist. Finally, the solution of the Schwarz-type BVP is explicitly obtained.