The Hardy inequality and the heat equation in twisted tubes
David Krejčiřı́k) Department of Theoretical Physics , Nuclear Physics Institute , Acad- emy of Sciences , 25068 Řež , Czech Republic;Enrique Zuazua) Basque Center for Applied Mathematics , Bizkaia Technology Park , Building 500 , 48160 Derio , Basque Country , Spain;
2009en
ABI
Annotatsiya
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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