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• W2949920795 abstract "We prove on-diagonal bounds for the heat kernel of the Dirichlet Laplacian $-Delta^D_Omega$ in locally twisted three-dimensional tubes $Omega$. In particular, we show that for any fixed $x$ the heat kernel decays for large times as $mathrm{e}^{-E_1t}, t^{-3/2}$, where $E_1$ is the fundamental eigenvalue of the Dirichlet Laplacian on the cross section of the tube. This shows that any, suitably regular, local twisting speeds up the decay of the heat kernel with respect to the case of straight (untwisted) tubes. Moreover, the above large time decay is valid for a wide class of subcritical operators defined on a straight tube. We also discuss some applications of this result, such as Sobolev inequalities and spectral estimates for Schrodinger operators $-Delta^D_Omega-V$." @default.
• W2949920795 created "2019-06-27" @default.
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• W2949920795 date "2011-05-04" @default.
• W2949920795 modified "2023-09-27" @default.
• W2949920795 title "Sharp two-sided heat kernel estimates of twisted tubes and applications" @default.
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• W2949920795 hasPublicationYear "2011" @default.
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