11. The Basic Elliptic PDEs in a Polygonal Domain
ATHANASSIOS S. FOKAS · Society for Industrial and Applied Mathematics eBooks · 2008
In this chapter we will derive integral representations for the basic elliptic PDEs in polygonal domains. These representations involve both the Dirichlet as well as the Neumann boundary values. For certain simple domains, by using the global relations it is possible to eliminate either the Dirichlet or the Neumann boundary values. This will be illustrated in Part IV.