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The boundary value problem for polyanalytic function in multiply- connected region. (English) Zbl 0613.30048

This paper is concerned with a boundary value problem for polyanalytic functions of order n in an m-connected plane domain. Conditions for the solvability of the problem are given, and for the representation of solutions a formula is derived involving solutions of certain Fredholm integral equations. Furthermore, under certain conditions, the existence of a unique solution is investigated.
(Remark: In the reviewer’s opinion, a demonstration of the practical usefulness of the results would be desirable.)
Reviewer: M.Kracht

MSC:

30G20 Generalizations of Bers and Vekua type (pseudoanalytic, \(p\)-analytic, etc.)
30G30 Other generalizations of analytic functions (including abstract-valued functions)
35J40 Boundary value problems for higher-order elliptic equations
35Q99 Partial differential equations of mathematical physics and other areas of application
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