Decomposition in regular and singular parts (in domains with corners) and stability under perturbation of the geometry
Tobias von Petersdorff, Ernst Peter Stephan · Applicable Analysis · 2014
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.