This article is cited in 6 papers

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

M. M. Sirazhudinov


Abstract: 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.

UDC: 517.95

MSC: 30E25, 35F15

Received: 17.02.1992

 English version: Russian Academy of Sciences. Sbornik. Mathematics, 1995, 80:2, 287–307

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