Abstract

This article aims to understand the locally periodic oscillating domain via unfolding operators. A three-dimensional rough domain Omega epsilon, epsilon >0 a small parameter, has been considered for the study where the boundary is rapidly oscillating with high amplitude. Though there are some articles with locally periodic boundary oscillations with small amplitude we do not see any literature with high-amplitude (O(1)) locally periodic oscillating domains. In this article, we attempt to study a problem in locally periodic rough domains with an eye towards the general oscillating domains without periodicity. With our experience of handling such domains and unfolding operators, we develop locally periodic unfolding operators to study our problems. We consider a nonlinear inhomogeneous Robin boundary value problem posed on this domain to demonstrate the utility of the newly defined operator.