Calculus of Variations and Geometric Measure Theory

L. Freddi - P. Hornung - M. G. Mora - R. Paroni

Stability of boundary conditions for the Sadowsky functional

created by mora on 22 Nov 2021
modified on 07 Jan 2022


Submitted Paper

Inserted: 22 nov 2021
Last Updated: 7 jan 2022

Year: 2021


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, as the width of the strip 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. This provides a rigorous justification of the original formal argument by Sadowsky about determining the equilibrium shape of a free-standing Möbius strip.

Keywords: Sadowsky functional, Elastic ribbons , Möbius band