Inserted: 20 nov 2018
Last Updated: 28 dec 2020
Journal: Advanced Studies in Pure Mathematics
in "The role of Metrics in the Theory of Partial Differential Equations", Proceedings of the "11th Mathematical Society of Japan Seasonal Institute" held in Sapporo in July 2018.
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.