Partial Differential and Integral Equations pp 193-205 | Cite as

# The Stability of the Riemann Boundary Value Problem for Vector Valued *M*-Analytic Functions

Chapter

## Abstract

In this paper, certain boundary value problems are solved in a Banach space which is defined by vector-valued regular solutions of the systemm *f* _{ x } + *M* *f* _{ y } = 0 of elliptic partial differential equations, where *M* is a constant *m* × *m* matrix without real eigenvalues and *f* is an *m* × *q* matrix. The properties of the integral of Cauchy type for vector-valued M-analytic functions are discussed. Next, the representation of the solutions of the Riemann boundary value problem and its pertubed problem for vector-valued M-analytic functions are presented.

## Keywords

Singular Integral Equation Finite Order Polynomial Matrix Elliptic Partial Differential Equation Cauchy Type
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## Copyright information

© Kluwer Academic Publishers 1999