Schwarz problem for higher order linear equations in a polydisc

Abstract

In this paper, we discuss the Schwarz boundary value problem for higher order linear complex differential equations in the unit polydisc of . After the relevant preparations, we give the solution for a model equation with homogeneous boundary conditions. Then we obtain the solutions of a linear equation involving Schwarz boundary conditions on the unit polydisc.

Keywords:

• Schwarz problem
• polydisc
• complex partial differential equations

AMS Subject Classifications:

• 32A26
• 32W50

Acknowledgements

The authors thank the referees for their comments and suggestions to improve this article.

Notes

No potential conflict of interest was reported by the authors.