Stability of boundary conditions for the Sadowsky functional

Abstract

It has been proved by the authors that the (extended) Sadowsky functional can be deduced as the Gamma-limit of the Kirchhoff energy on a rectangular strip of height $\epsilon$, as $\epsilon$ tends to 0. In this paper we show that this Gamma-convergence result is stable when affine boundary conditions are prescribed on the short sides of the strip. These boundary conditions include those corresponding to a Möbius band.