Boundary value problems for generalized Cauchy-Riemann systems in the space. (English) Zbl 0792.35022

Kühnau, R. (ed.) et al., Boundary value and initial value problems in complex analysis: studies in complex analysis and its applications to partial differential equations 1. Papers from the 5th conference on complex analysis, held in Halle, Germany, in December 1988. Harlow: Longman Scientific & Technical. Pitman Res. Notes Math. Ser. 256, 159-183 (1991).
Summary: The present paper deals with the Riemann-Hilbert boundary value problem. The methodic foundations for a systematic approach are the theory of group representations and the the theory of elliptic differential equations in Sobolev spaces. We give an explicit description of the shape of the generalized Cauchy-Riemann systems and a criterion for the Fredholm property of the boundary value problem. In subsequent papers there will be investigated the existence of Fredholm boundary value problems, the adjoint boundary value problem and direct methods.
For the entire collection see [Zbl 0771.00035].


35E20 General theory of PDEs and systems of PDEs with constant coefficients
32V05 CR structures, CR operators, and generalizations
11E88 Quadratic spaces; Clifford algebras