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The construction of periodic unfolding operators on some compact Riemannian manifolds

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  • Sören Dobberschütz
  • Michael Böhm

The notion of periodic unfolding has become a standard tool in the theory of periodic homogenization. However, all the results obtained so far are only applicable to the "flat" Euclidean space R n. In this paper, we present a generalization of the method of periodic unfolding applicable to structures defined on certain compact Riemannian manifolds. While many results known from unfolding in domains of R n can be recovered, for the unfolding of gradients a transport operator has to be defined. This operator connects vector fields on the manifold and in the reference cell, which allows for the formulation of general two-scale problems. We illustrate the use of the new unfolding technique with a simple elliptic model-problem.

OriginalsprogEngelsk
TidsskriftAdvances in Pure and Applied Mathematics
Vol/bind5
Udgave nummer1
Sider (fra-til)31-45
Antal sider15
ISSN1867-1152
DOI
StatusUdgivet - 2014

ID: 131889496