On the Singular Eigenfunctions for Plane Harmonic Problems in Composite Regions

Abstract

This paper is concerned with the singular behavior of harmonic functions at the vertex of a plane, composite, wedge region. Separable harmonic functions which include logarithmic terms are investigated for their possible existence in the vicinity of the vertex. The eigenequations governing existence are examined and explicit determination of the singular eigenvalues made for several combinations of boundary and interface conditions. The results enable an appreciation of the possible singular nature in such problems which aids any complete (numerical) analysis.