Abstract:
In this talk we propose a stochastic interpretation of
a recently established Hardy inequality in twisted tubes.
Roughly speaking, we show that Brownian particles
in an infinite three-dimensional tube of uniform cross-section
and absorbing boundary conditions die in a sense more easily
if the tube is twisted. This is far from being obvious
since the average exit time of the Brownian particle is
the same in twisted and untwisted tubes.
More precisely, we study the asymptotic behaviour of
solutions of the heat equation in twisted tubes
and prove that the geometric deformation of twisting
yields an improved decay rate for the heat semigroup.
This is a joint work with Enrique Zuazua.
