Journal
KODAI MATHEMATICAL JOURNAL
Volume 37, Issue 2, Pages 453-474Publisher
KINOKUNIYA CO LTD
DOI: 10.2996/kmj/1404393898
Keywords
elastica; p-Laplacian; generalized complete elliptic integrals; flat-core solution
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Funding
- Japan Society for the Promotion of Science [24540199]
- Grants-in-Aid for Scientific Research [24540199] Funding Source: KAKEN
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Planar elastica problem is a classical but has broad connections with various fields, such as elliptic functions, differential geometry, soliton theory, material mechanics, etc. This paper regards classical elastica as a theory corresponding to Lebesgue L-2 case, and extends it to L-p cases. For the sake of the effect of p-Laplacian, novel curious solutions appear especially for cases p > 2. These solutions never appear in 1 < p <= 2 cases and we call them flat-core solutions according to Takeuchi [6, 7].
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