Smooth Homogenization of Heat Equations on Tubular Neighborhoods

Details Smooth Homogenization of Heat Equations on Tubular Neighborhoods Smooth Homogenization of Heat Equations on Tubular Neighborhoods

2008-10-28

arxiv.org/abs/0810.5052v1

Mathematics

Analysis of PDEs

30 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 diameter tends to zero, a suitably rescaled and renormalized semigroup
converges to a limit semigroup in Sobolev spaces of arbitrarily large Sobolev
index.

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