TY - JOUR
T1 - The critical points of the elastic energy among curves pinned at endpoints
AU - Yoshizawa, Kensuke
N1 - Funding Information:
2020 Mathematics Subject Classification. Primary: 49K15, 53A04; Secondary: 34A05. Key words and phrases. Euler’s elastica, boundary value problem, shooting method. The author was supported by Grant-in-Aid for JSPS Fellows 19J2074.
Publisher Copyright:
© 2022 American Institute of Mathematical Sciences. All rights reserved.
PY - 2022/1
Y1 - 2022/1
N2 - In this paper we find curves minimizing the elastic energy among curves whose length is fixed and whose ends are pinned. Applying the shooting method, we can identify all critical points explicitly and determine which curve is the global minimizer. As a result we show that the critical points consist of wavelike elasticae and the minimizers do not have any loops or interior inection points.
AB - In this paper we find curves minimizing the elastic energy among curves whose length is fixed and whose ends are pinned. Applying the shooting method, we can identify all critical points explicitly and determine which curve is the global minimizer. As a result we show that the critical points consist of wavelike elasticae and the minimizers do not have any loops or interior inection points.
UR - http://www.scopus.com/inward/record.url?scp=85120614721&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85120614721&partnerID=8YFLogxK
U2 - 10.3934/dcds.2021122
DO - 10.3934/dcds.2021122
M3 - Article
AN - SCOPUS:85120614721
SN - 1078-0947
VL - 42
SP - 403
EP - 423
JO - Discrete and Continuous Dynamical Systems
JF - Discrete and Continuous Dynamical Systems
IS - 1
ER -