The double layer potential operator over polyhedral domains i: solvability in weighted sobolev spaces

Abstract

We consider the integral equation, (λ-K)u=f, where K is the double layer (harmonic) potential operator on the boundary of a bounded polyhedron in R³ and λ∣λ∣≥1 is a complex constant. We study the mapping properties of λ - K in weighted Sobolev spaces, applying Mellin transformation techniques directly to the integral equation.

Keywords:

• Double layer
• potential theory

AMS:

• 31B10

Additional information

Notes on contributors

Johannes Elschner

Dedicated to Professor Erhard Meister on the occasion of his 60th birthday