Two-scale convergence in thin domains with locally periodic rapidly oscillating boundary

The aim of this paper is to adapt the notion of two-scale convergence in Lp to the case of a measure converging to a singular one. We present a specific case when a thin cylinder with locally periodic rapidly oscillating boundary shrinks to a segment, and the corresponding measure charging the cylinder converges to a one-dimensional Lebegues measure of an interval. Themethod is then applied to the asymptotic analysis of linear elliptic operators with locally periodic coefficients andap-Laplacian stated inthincylinders withlocally periodic rapidly varying thickness