arXiv:0906.3359 Abstract | arXiv Analytics

arXiv:0906.3359 [math.AP]Abstract References Reviews Resources

The Hardy inequality and the heat equation in twisted tubes

Published 2009-06-18, updated 2009-06-22Version 2

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.

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

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

Categories: math.AP, math-ph, math.MP, math.SP

Keywords: heat equation, hardy inequality, twisted tubes, dirichlet laplacian, proof employs hardy inequalities

Tags: journal article

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