Geodesic
A function theorety method in elliptic problems in the plane. II.~The piecewise smooth case
Izvestiya. Mathematics , Tome 40 (1993) no. 3, pp. 529-563

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A general boundary value problem, encompassing from a unified viewpoint a broad circle of local and nonlocal boundary value problems, is studied for elliptic systems with real, constant (and only leading) matrix coefficients. A method is given for the equivalent reduction of this problem to a system of boundary equations. The considerations are carried out in domains with piecewise smooth boundaries and in weighted spaces. A Noetherian criterion and an index formula for this problem are established, and the asymptotics of its solution in a neighborhood of corner points is described. 
@article{IM2_1993_40_3_a3,
     author = {A. P. Soldatov},
     title = {A function theorety  method in elliptic problems in the plane. {II.~The} piecewise smooth case},
     journal = {Izvestiya. Mathematics },
     pages = {529--563},
     publisher = {mathdoc},
     volume = {40},
     number = {3},
     year = {1993},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1993_40_3_a3/}
}
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A. P. Soldatov. A function theorety  method in elliptic problems in the plane. II.~The piecewise smooth case. Izvestiya. Mathematics , Tome 40 (1993) no. 3, pp. 529-563. http://geodesic.mathdoc.fr/item/IM2_1993_40_3_a3/