The Hardy inequality and the heat equation in twisted tubes

@article{Krejik2009TheHI,
  title={The Hardy inequality and the heat equation in twisted tubes},
  author={David Krej{\vc}iř{\'i}k and Enrique Zuazua},
  journal={Journal de Math{\'e}matiques Pures et Appliqu{\'e}es},
  year={2009},
  volume={94},
  pages={277-303}
}
  • David Krejčiřík, Enrique Zuazua
  • Published 2009
  • Mathematics, Physics
  • Journal de Mathématiques Pures et Appliquées
  • 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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