Polyharmonic Robin problem for complex linear partial differential equations

Abstract

In this article, generalized polyharmonic Robin functions are introduced together with some of their properties. A hierarchy of integral operators with relevant kernel functions are investigated. These operators are used to transform the Robin problem for a th order linear partial complex differential equation with polyharmonic leading term (generalized -Poisson equation) into a singular integral equation having Fredholm property.

Keywords:

• polyharmonic Robin function
• Robin problem
• elliptic higher order complex partial differential equations

AMS Subject Classifications:

• 31A30
• 31A10
• 31A25

Acknowledgments

The authors are grateful to the referees for their valuable comments which improved the article.