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arXiv · 1703.09027

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

Irina Pettersson
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Abstract

The aim of this paper is to adapt the notion of two-scale convergence in $L^p$ 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. The method is then applied to the asymptotic analysis of linear elliptic operators with locally periodic coefficients in a thin cylinder with locally periodic rapidly varying thickness.

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Irina Pettersson. 2017-03-27. Two-scale convergence in thin domains with locally periodic rapidly oscillating boundary. https://arxiv.org/abs/1703.09027

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