Geodesic
On the Riemann--Hilbert problem for first order elliptic systems in multiply connected domains
Sbornik. Mathematics, Tome 80 (1995) no. 2, pp. 287-307

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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. 
@article{SM_1995_80_2_a2,
     author = {M. M. Sirazhudinov},
     title = {On the {Riemann--Hilbert} problem for first order elliptic systems in multiply connected domains},
     journal = {Sbornik. Mathematics},
     pages = {287--307},
     publisher = {mathdoc},
     volume = {80},
     number = {2},
     year = {1995},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1995_80_2_a2/}
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M. M. Sirazhudinov. On the Riemann--Hilbert problem for first order elliptic systems in multiply connected domains. Sbornik. Mathematics, Tome 80 (1995) no. 2, pp. 287-307. http://geodesic.mathdoc.fr/item/SM_1995_80_2_a2/