Dirichlet Laplacian in a thin twisted strip

Abstract

Let [Formula: see text] be a two-dimensional, infinite and twisted strip in [Formula: see text]. Consider [Formula: see text] the Dirichlet Laplacian operator in [Formula: see text]. At first, we find the effective operator when the transversal sections of [Formula: see text] tend to zero. Then, assuming that [Formula: see text] is thin enough, we show some situations where the discrete spectrum [Formula: see text] is nonempty; an asymptotic behavior for the eigenvalues is also found. In particular, we study the case where the twisted effect “grows” at infinity.