|Titolo||Sharp two-sided heat kernel estimates of twisted tubes and applications|
|Autore/i||Grillo, G.; Kovarik, H.; Pinchover, Y.|
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|Abstract||We prove sharp on-diagonal bounds for the heat kernel of the Dirichlet Laplacian in locally twisted three-dimensional tubes. Such bounds show 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 Schroedinger operators.