The Hardy inequality and the heat equation in twisted tubes
Abstract
We show that a twist of a threedimensional tube of uniform crosssection yields an improved decay rate for the heat semigroup associated with the Dirichlet Laplacian in the tube. The proof employs Hardy inequalities for the Dirichlet Laplacian in twisted tubes and the method of selfsimilar variables and weighted Sobolev spaces for the heat equation.
 Publication:

arXiv eprints
 Pub Date:
 June 2009
 arXiv:
 arXiv:0906.3359
 Bibcode:
 2009arXiv0906.3359K
 Keywords:

 Mathematics  Analysis of PDEs;
 Mathematical Physics;
 Mathematics  Spectral Theory
 EPrint:
 35 pages, LaTeX with 2 EPS figures