Decomposition in regular and singular parts (in domains with corners) and stability under perturbation of the geometry

Abstract

We analyze the Dirichlet problem for the Laplacian in a polygonal domain where boundary and angles depend on a parameter. We use the boundary integral equation, localization and Mellin transformation techniques to show that the solution has a decomposition in regular and singular parts which blow up at certain exceptional angles. We derive a modified decomposition which depends continuously on the angle.

Keywords:

• corner singularities
• Mellin transformation
• boundary integral equations

Notes

Dedicated to the occasion of Prof. Martin Costabel’s 65th birthday.