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Del Nin, Giacomo, Pluda, Alessandra and Pozzetta, Marco (2020) Degenerate elastic networks. The Journal of Geometric Analysis . doi:10.1007/s12220-020-00521-z ISSN 1050-6926.
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Official URL: https://doi.org/10.1007/s12220-020-00521-z
Abstract
We minimize a linear combination of the length and the L2-norm of the curvature among networks in Rd belonging to a given class determined by the number of curves, the order of the junctions, and the angles between curves at the junctions. Since this class lacks compactness, we characterize the set of limits of sequences of networks bounded in energy, providing an explicit representation of the relaxed problem. This is expressed in terms of the new notion of degenerate elastic networks that, rather surprisingly, involves only the properties of the given class, without reference to the curvature. In the case of d=2 we also give an equivalent description of degenerate elastic networks by means of a combinatorial definition easy to validate by a finite algorithm. Moreover we provide examples, counterexamples, and additional results that motivate our study and show the sharpness of our characterization.
| Item Type: | Journal Article | ||||||
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| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
| Library of Congress Subject Headings (LCSH): | Elasticity -- Mathematical models, Geometric analysis, Spline theory, Approximation theory | ||||||
| Journal or Publication Title: | The Journal of Geometric Analysis | ||||||
| Publisher: | Springer New York LLC | ||||||
| ISSN: | 1050-6926 | ||||||
| Official Date: | 9 October 2020 | ||||||
| Dates: |
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| DOI: | 10.1007/s12220-020-00521-z | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||
| Date of first compliant deposit: | 12 November 2020 | ||||||
| Date of first compliant Open Access: | 13 November 2020 | ||||||
| RIOXX Funder/Project Grant: |
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