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In this paper, we show that this <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\Gamma $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u0393<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-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 M\u00f6bius band. This provides a rigorous justification of the original formal argument by Sadowsky about determining the equilibrium shape of a free-standing M\u00f6bius strip. We further write the equilibrium equations for the limit problem and show that, under some regularity assumptions, the centerline of a developable M\u00f6bius band at equilibrium cannot be a planar curve.\n<\/jats:p>","DOI":"10.1007\/s00332-022-09829-2","type":"journal-article","created":{"date-parts":[[2022,8,17]],"date-time":"2022-08-17T19:02:29Z","timestamp":1660762949000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Stability of Boundary Conditions for the Sadowsky Functional"],"prefix":"10.1007","volume":"32","author":[{"given":"Lorenzo","family":"Freddi","sequence":"first","affiliation":[]},{"given":"Peter","family":"Hornung","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7456-0065","authenticated-orcid":false,"given":"Maria Giovanna","family":"Mora","sequence":"additional","affiliation":[]},{"given":"Roberto","family":"Paroni","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,8,17]]},"reference":[{"key":"9829_CR1","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1090\/qam\/652052","volume":"40","author":"JC Alexander","year":"1982","unstructured":"Alexander, J.C., Antman, S.S.: The ambiguous twist of Love. 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