In this paper, the Schwarz boundary value problem (BVP) for the inhomogeneous Cauchy-Riemann equation in a triangle is investigated explicitly. Firstly, by the technique of parquetingreflection and the Cauchy-Pompeiu representation formula a modified Cauchy-Schwarz representation formula is obtained. Then, the solution of the Schwarz BVP is explicitly solved. In particular, the boundary behavio...

Over the last two decades, classical Schwarz methods have been extended to systems of hyperbolic partial differential equations, and it was observed that the classical Schwarz method can be convergent even without overlap in certain cases. This is in strong contrast to the behavior of classical Schwarz methods applied to elliptic problems, for which overlap is essential for convergence. Over th...

The Schwarz Alternating Method can be used to solve elliptic boundary value problems on domains which consist of two or more overlapping subdomains. The solution is approximated by an innnite sequence of functions which results from solving a sequence of elliptic boundary value problems in each of the subdomains. In this paper, proofs of convergence of some Schwarz Alternating Methods for nonli...