PLANAR p-ELASTIC CURVES AND RELATED GENERALIZED COMPLETE ELLIPTIC INTEGRALS

摘要

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].