• Mathematics
  • Published 2008

L2-Homogenization of Heat Equations on Tubular Neighborhoods

@inproceedings{Wittich2008L2HomogenizationOH,
  title={L2-Homogenization of Heat Equations on Tubular Neighborhoods},
  author={Olaf Wittich},
  year={2008}
}
We consider the heat equation with Dirichlet boundary conditions on the tubular neighborhood of a closed Riemannian submanifold of a Riemannian manifold. 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. 

References

Publications referenced by this paper.
SHOWING 1-10 OF 17 REFERENCES

An Introduction to-convergence

VIEW 3 EXCERPTS
HIGHLY INFLUENTIAL

H

N. A. Sidorova, O. G. Smolyanov
  • v. Weizsäcker and O. Wittich. The surface limit of Brownian motion in tubular neighborhoods of an embedded Riemannian manifold J. Funct. Anal., 206(2): 391 – 413
  • 2004
VIEW 2 EXCERPTS

Partial Differential Equations I: Basic Theory

M. E. Taylor
  • volume 23 of Texts in Applied Mathematics. Springer, New York, 1st edition
  • 1999

Riemannian Geometry

T. Sakai
  • AMS, Providence, RI
  • 1997