Direct methods for generalized Cauchy-Riemann systems in the space. (English) Zbl 0824.30030

Summary: This paper is a continuation of the author’s thesis reviewed in Zbl 0723.30034 and the author’s paper in ibid. 21, No. 1-2, 19-38 (1993; Zbl 0741.30039), where the Fredholm property for boundary value problems of Riemann-Hilbert type was investigated. At first we give a short summary of previous results needed here. The adjoined boundary value problem is introduced in Section 2, and several connections between the two boundary value problems are derived. These will be used in Section 3, where we treat direct methods. There will be established sufficient conditions, which imply the uniqueness of the solution and the solvability for arbitrary right-hand sides.


30G35 Functions of hypercomplex variables and generalized variables
35F15 Boundary value problems for linear first-order PDEs
35J50 Variational methods for elliptic systems
35J55 Systems of elliptic equations, boundary value problems (MSC2000)
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