On the Riemann–Hilbert problem for first order elliptic systems in multiply connected domains

The Riemann–Hilbert problem for arbitrary first-order elliptic systems with continuous coefficients in the principal part in multiply connected domains is studied. The problem is considered both in Sobolev and Hölder spaces, and a condition for the Fredholm property and a formula for the index are obtained. Also considered are refinements of the differential properties of solutions depending on the properties of the coefficients, the right-hand sides, and the boundary of the domain.