Abstract
We consider planar networks minimizing the elastic energy, we state an existence and regularity result, and we discuss some geometric properties of minimal configurations. We also consider the evolution of networks by the gradient flow of the energy, and we give a well-posedness result in the case of natural boundary conditions.
Information
Published: 1 January 2020
First available in Project Euclid: 29 December 2020
Digital Object Identifier: 10.2969/aspm/08510325
Subjects:
Primary:
35A15
Secondary:
35K52
,
49Q10
,
53C44
Keywords:
elastic energy
,
geometric evolution equations
,
minimization problems involving curvature
,
networks
,
parabolic systems of fourth order
,
singular structures
,
Willmore flow
Rights: Copyright © 2020 Mathematical Society of Japan
