The Hardy inequality and the heat equation in twisted tubes

Details The Hardy inequality and the heat equation in twisted tubes The Hardy inequality and the heat equation in twisted tubes

2009-06-18

arxiv.org/abs/0906.3359v2

J. Math. Pures Appl. 94 (2010), 277-303

Mathematics

Analysis of PDEs

35 pages, LaTeX with 2 EPS figures; a misprint in Conjecture on page 33 corrected

Scientific paper

We show that a twist of a three-dimensional tube of uniform cross-section
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 self-similar variables
and weighted Sobolev spaces for the heat equation.

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