Calculus of Variations and Geometric Measure Theory

G. Bevilacqua - C. Lonati

Effects of surface tension and elasticity on critical points of the Kirchhoff-Plateau problem

created by bevilacqua on 14 Feb 2023
modified on 28 Nov 2023


Published Paper

Inserted: 14 feb 2023
Last Updated: 28 nov 2023

Journal: Bollettino dell Unione Matematica Italiana
Year: 2023
Doi: 10.1007/s40574-023-00392-6

ArXiv: 2302.06269 PDF


We introduce a modified Kirchhoff-Plateau problem adding an energy term to penalize shape modifications of the cross-sections appended to the elastic midline. We prove the existence of minimizers applying the Direct Method of the Calculus of Variations. Then, choosing three different geometrical shapes for the cross-section, we derive Euler-Lagrange equations for a planar version of the Kirchhoff-Plateau problem. We show that in the physical range of the parameters, there exists a unique critical point satisfying the imposed constraints. Finally, we analyze the effects of the surface tension on the shape of the cross-sections at the equilibrium.