1. FORMULATION OF SINGULAR MODIFIED RIEMANN-HILBERT BOUNDARY VALUE PROBLEMS FOR ELLIPTIC COMPLEX EQUATIONS OF FIRST ORDER

Abstract: In [1], the author first proposed a well-posedness of singular Riemann-Hilbert boundary value problem for generalized analytic functions in multiply con-nected domains, and the well posedness allows that the solutions of the modified problem possess some poles in N + 1-connected domain D. In [3], the author proposed another well-posedness of the Riemann-Hilbert boundary value problem with continuous solutions for nonlinear elliptic complex equations of first order, in particular the well-posedness includes the well-posedness of the singular case of 0 < K < N. Recently, the authors of this paper proposes three kinds of new well-posedness of singular Riemann-Hilbert boundary value problem for nonlinear elliptic complex equations of first order in multiply connected domains. We shall prove the existence of solutions for these boundary value problems