Abstract
In this article, we first propose the Riemann–Hilbert problem for uniformly elliptic complex equations of first order in multiply connected domains and its new well-posed-ness with continuous solutions. Then we obtain a priori estimates of solutions of the modified Riemann–Hilbert problem, and derive the solvability results of the modified and original Riemann–Hilbert problems. Finally we shall verify the equivalence of two kinds of well-posed-ness for the Riemann–Hilbert boundary value problem.
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