Holomorphic Extension Theorems in Lipschitz Domains of C2

The holomorphic functions of several complex variables are closely related to the continuously differentiable solutions f : R-2n bar right arrow C-n of the so-called isotonic system partial derivative((x) under bar1) + i((f) over tilde2) = 0. The aim of this paper is to bring together these two areas which are intended as a good generalization of the classical one-dimensional complex analysis. In particular, it is of interest to study how far some classical holomorphic extension theorems can be stretched when the regularity of the boundary is reduced from C-1-smooth to Lipschitz. As an illustration, we give a complete viewpoint on simplified proofs of Kytmanov-Aronov-Aizenberg type theorems for the case n = 2.