On the existence of Fredholm boundary value problems for generalized Cauchy-Riemann systems in the space. (English) Zbl 0741.30039

Stern, Iris

Complex Variables, Theory Appl. 21, No. 1-2, 19-38 (1993).

The paper deals with the Riemann-Hilbert boundary value problem for generalized Cauchy-Riemann systems in the space. We investigate the question about existence or non-existence of Fredholm boundary value problems in dependence on the structure of the Cauchy-Riemann system. For this purpose we use a result of a previous paper, stating a criterion for the Fredholm property of a boundary value problem. The obtained conclusions allow a decision of the existence problem for the majority of all generalized Cauchy-Riemann systems. They contain many results of other authors as special cases.

Reviewer: I.Stern

MSC:

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

Keywords:

Riemann-Hilbert boundary value problem; Fredholm boundary value problems