A unique graph of minimal elastic energy
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- by Anders Linnér and Joseph W. Jerome PDF
- Trans. Amer. Math. Soc. 359 (2007), 2021-2041 Request permission
Abstract:
Nonlinear functionals that appear as a product of two integrals are considered in the context of elastic curves of variable length. A technique is introduced that exploits the fact that one of the integrals has an integrand independent of the derivative of the unknown. Both the linear and the nonlinear cases are illustrated. By lengthening parameterized curves it is possible to reduce the elastic energy to zero. It is shown here that for graphs this is not the case. Specifically, there is a unique graph of minimal elastic energy among all graphs that have turned 90 degrees after traversing one unit.References
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Additional Information
- Anders Linnér
- Affiliation: Department of Mathematical Sciences, Northern Illinois University, DeKalb, Illinois 60115
- Email: alinner@math.niu.edu
- Joseph W. Jerome
- Affiliation: Department of Mathematics, Northwestern University, Evanston, Illinois 60208
- Email: jwj@math.northwestern.edu
- Received by editor(s): January 12, 2005
- Published electronically: December 15, 2006
- Additional Notes: The research for this paper was essentially completed during the first author’s sabbatical year at Northwestern.
The second author’s research was supported in part by NSF grant DMS-0311263 - © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 359 (2007), 2021-2041
- MSC (2000): Primary 58E25, 49J30; Secondary 58Z05
- DOI: https://doi.org/10.1090/S0002-9947-06-04315-7
- MathSciNet review: 2276610