Weighted analytic regularity in polyhedra

Abstract

We explain a simple strategy to establish analytic regularity for solutions of second order linear elliptic boundary value problems. The abstract framework presented here helps to understand the proof of analytic regularity in polyhedral domains given in the authors’ paper in [M. Costabel, M. Dauge, S. Nicaise, Analytic regularity for linear elliptic systems in polygons and polyhedra, Math. Models Methods Appl. Sci. 22 (8) (2012)]. We illustrate this strategy by considering problems set in smooth domains, in corner domains and in polyhedra.