Inserted: 16 apr 2019
Last Updated: 4 mar 2020
Journal: Calc. Var. Partial Differential Equations
We study an old variational problem formulated by Euler as Proposition 53 of his “Scientia Navalis" by means of the direct method of the calculus of variations. Precisely, through relaxation arguments, we prove the existence of minimizers. We fully investigate the analytical structure of the minimizers in dependence of the geometric parameters and we identify the ranges of uniqueness and non-uniqueness.