On the precise asymptotics of the constant in Friedrich's inequality for functions vanishing on the part of the boundary with microinhomogeneous structure

We construct the asymptotics of the sharp constant in the Friedrich-type inequality for functions, which vanish on the small part of the boundary Gamma(epsilon)(l). It is assumed that Gamma(epsilon)(l) consists of (1/delta)(n-1) pieces with diameter of order O(epsilon delta). In addition, delta = delta(epsilon) and delta -> 0 as epsilon -> 0. Copyright (C) 2007.