TY - JOUR
T1 - Structure and classification results for the ∞-elastica problem
AU - Moser, Roger
N1 - Accepted for publication in the American Journal of Mathematics.
PY - 2021/7/27
Y1 - 2021/7/27
N2 - Consider the following variational problem: among all curves in Rn of fixed length with prescribed end points and prescribed tangents at the end points, minimise the L∞-norm of the curvature. We show that the solutions of this problem, and of a generalised version, are characterised by a system of differential equations. Furthermore, we have a lot of information about the structure of solutions, which allows a classification.
AB - Consider the following variational problem: among all curves in Rn of fixed length with prescribed end points and prescribed tangents at the end points, minimise the L∞-norm of the curvature. We show that the solutions of this problem, and of a generalised version, are characterised by a system of differential equations. Furthermore, we have a lot of information about the structure of solutions, which allows a classification.
M3 - Article
JO - American Journal of Mathematics
JF - American Journal of Mathematics
SN - 0002-9327
ER -
