On smooth images of oscillating surfaces of solids

An asymptotic analysis of solutions to elliptic problems in domains with rapidly oscillating boundaries (rough and damaged surfaces) will be presented. The construction of several asymptotic terms, including boundary layers, permit for modelling the problem by a much simpler problem, solution of which, nevertheless, gives the two-term asymptotics of the original solution. Two approaches for this type of modelling will be discussed. For the sake of simplicity, boundary value problems for a scalar equation will be considered, although the investigation is directed to the elasticity theory.