L2-Homogenization of Heat Equations on Tubular Neighborhoods

Details L2-Homogenization of Heat Equations on Tubular Neighborhoods L2-Homogenization of Heat Equations on Tubular Neighborhoods

2008-10-28

arxiv.org/abs/0810.5047v1

Mathematics

Analysis of PDEs

34 pages

Scientific paper

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.

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