This article is cited in 16 papers

A function theorety method in elliptic problems in the plane. II. The piecewise smooth case

A. P. Soldatov

Scientific Research Institute of Applied Mathematics and Automation, Kabardino-Balkar Scientific Centre of the Russian Academy of Sciences

Abstract: 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.

UDC: 517.9

MSC: Primary 35J30; Secondary 30E25, 35B40

Received: 25.04.1991

 English version: Russian Academy of Sciences. Izvestiya Mathematics, 1993, 40:3, 529–563

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