Abstract:
The Dirichlet Laplacian in a curved two-dimensional strip built along a
plane curve is investigated in the limit when the uniform cross-section
of the strip diminishes. We show that the Laplacian converges in a strong
resolvent sense to the well known one-dimensional Schroedinger operator
whose potential is expressed solely in terms of the curvature of the
reference curve. In comparison with previous results we allow curves
which are unbounded and whose curvature is not differentiable. This is a
joint work with David Krejèiøík.
