On boundary-value problems in domains perforated along manifolds

Abstract

Using the unfolding technique, developed in reactor physics, we have developed a method for calculating the frequency distribution function for materials starting from the measured data on the temperature variation of specific heat at constant volume. As examples we have considered the cases of the following materials: graphite, selenium, tellurium, polyethylene and SiO, glass. In the case of graphite the frequency distribution function has been used to calculate the low-energy neutron scattering cross section with encouraging results. K X = Y(3)

Averaging of variational inequalities for the Laplacian with nonlinear restrictions along manifolds

“…Lemmas 1 and 2 in [7] and Lemma 1 in [5], respectively, for their proofs; see also [8]). In the lemmas below, and in what follows, C denotes a constant independent of ".…”

“…This choice implies introducing new local problems (3.4) and (4.6) on the unit cell "(À1/2, 1/2) n na " G 0 (cf. [5,8] for related problems) and obtaining precise bounds for their solutions. Also, note that, for 2 [1, (n À 1)/(n À 2)), the asymptotic behaviour of the solution u " , as " !…”

Integral Methods in Science and Engineering

“…Also, in these lemmas, the constant C does not depend on the functions w appearing in their statements. See Lemma 1 in [OlSh95a] and Lemma 1 in [LoEtAl97] for the proof of Lemma 1 and 2, respectively.…”

“…III.4 of [OlShYo92] (cf. also [LoEtAl97] and [OlSh95a] for further references). For the sake of completeness, we introduce a general strong result from the spectral perturbation theory: see Theorems 1.4 and 1.7 in Chap.…”

“…As a matter of fact, asymptotics for the eigenvalues of (11.1) for the case of one single hole has been considered in, e.g., [Ro93]; for a spatial distribution of the holes periodically distributed let us mention [OlSh95b]; similarly, for a two-dimensional domain and κ ∈ (0, 1) we refer to [Oz96]. For the geometrical configuration here considered and κ = 0 we mention [LoEtAl97]. Let us refer to the above-mentioned papers for further references on spectral problems in perforated domains.…”