1 Administration, Department of Chemistry, Faculty of Science, Københavns Universitet 2 Department of Chemistry, Faculty of Science, Københavns Universitet 3 University of Bremen 4 Department of Chemistry, Faculty of Science, Københavns Universitet 5 University of Bremen
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. © 2014 by Walter de Gruyter Berlin/Boston 2014.
Advances in Pure and Applied Mathematics, 2014, Vol 5, Issue 1, p. 31-45
homogenization; Periodic unfolding; Riemannian manifolds
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