On Asymptotics of Solutions of Elliptic Mixed Boundary Value Problems of Second-Order in Domains with Vanishing Edges

Abstract

This paper investigates the behavior of variational solutions of second-order elliptic mixed boundary value problems (MBVP) with real coefficients in n-dimensional domains with edges near the points where the edges are vanishing. It is shown that the first coefficient involved in the decomposition of the solution into regular and singular part can be extended continuously in appropriate spaces across such points, thus showing that the standard decomposition formula holds also in such domains.