Schwarz problem in lens and half lens

We consider the Schwarz boundary value problem (BVP) for the inhomogeneous Cauchy–Riemann equation in lenses and half lenses. By the technique of parqueting–reflection and the Cauchy–Pompeiu representation formula for lenses and half lenses, the Cauchy–Schwarz representation formula is obtained. Also, the solution of the Schwarz BVP is explicitly obtained.