# 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}
}```
• 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.

#### Citations

##### Publications citing this paper.
SHOWING 1-10 OF 47 CITATIONS

## The Hardy inequality and the heat flow in curved wedges

VIEW 4 EXCERPTS
CITES BACKGROUND & METHODS

## Hardy Inequalities in Globally Twisted Waveguides

• Mathematics, Physics
• 2014
VIEW 3 EXCERPTS
CITES METHODS & BACKGROUND

## Hardy inequalities with boundary singularities

VIEW 1 EXCERPT
CITES BACKGROUND

## The Brownian traveller on manifolds

• Mathematics, Physics
• 2011
VIEW 4 EXCERPTS
CITES BACKGROUND & METHODS

## Spectral estimates for Dirichlet Laplacian on tubes with exploding twisting velocity

• Mathematics, Physics
• 2018
VIEW 1 EXCERPT

## Spectral estimates for Dirichlet Laplacians and Schroedinger operators on geometrically nontrivial cusps

• Mathematics, Physics
• 2012

## The Hardy inequality and the heat equation with magnetic field in any dimension

• Mathematics, Physics
• 2014
VIEW 3 EXCERPTS
CITES BACKGROUND & METHODS

## The asymptotic behaviour of the heat equation in a twisted Dirichlet-Neumann waveguide

• Mathematics, Physics
• 2010
VIEW 6 EXCERPTS
CITES BACKGROUND & METHODS

## Large time behavior of the heat kernel of two-dimensional magnetic Schroedinger operators

2009
2020

### CITATION STATISTICS

• 2 Highly Influenced Citations

#### References

##### Publications referenced by this paper.
SHOWING 1-10 OF 29 REFERENCES

## A Hardy inequality in a twisted Dirichlet-Neumann waveguide

• Physics, Mathematics
• 2006

## Hardy inequalities in strips on ruled surfaces

VIEW 1 EXCERPT

## A Hardy Inequality in Twisted Waveguides

• Physics, Mathematics
• 2008

## Spectrum of the Schrödinger Operator in a Perturbed Periodically Twisted Tube

• Physics, Mathematics
• 2005

## The Hardy Inequality and the Asymptotic Behaviour of the Heat Equation with an Inverse-Square Potential

• Mathematics
• 2000
VIEW 1 EXCERPT

## Dirichlet problems on varying domains

VIEW 1 EXCERPT

## On the spectrum of the Dirichlet Laplacian in a narrow strip

• Mathematics
• 2007

## Asymptotic expansion for damped wave equations with periodic coefficients

• Mathematics
• 2001
VIEW 1 EXCERPT

## Large time behavior in \mathbb{R}^N for linear parabolic equations with periodic coefficients

• Mathematics
• 2000