Abstract
We apply the parqueting-reflection technique for a triangle domain to achieve the points of the complex plane. Then the Cauchy–Schwarz representation formula is construed by the Cauchy–Pompeiu formula and an explicit solution for the Schwarz boundary value problem (BVP) for the non-homogeneous Cauchy–Riemann equation on the triangle is presented. We also discuss the condition of solvability and by using the Schwarz BVP, the inhomogeneous Dirichlet and homogeneous Neumann BVPs are investigated.
Disclosure statement
No potential conflict of interest was reported by the author(s).