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arXiv:0810.5047 [math.AP]AbstractReferencesReviewsResources

L2-Homogenization of Heat Equations on Tubular Neighborhoods

O. Wittich

Published 2008-10-28Version 1

We consider the heat equation with Dirichlet boundary conditions on the tubular neighborhood of a closed Riemannian submanifold. We show that, as the tube radius decreases, the semigroup of a suitably rescaled and renormalized generator can be effectively described by a Hamiltonian on the submanifold with a potential that depends on the geometry of the submanifold and of the embedding.

Comments: 34 pages
Categories: math.AP, math.PR
Subjects: 35K05, 74Q10
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