Calculus of Variations and Geometric Measure Theory

F. Maddalena - E. Mainini - D. Percivale

Euler's optimal profile problem

created by mainini on 16 Apr 2019
modified on 04 Mar 2020

[BibTeX]

Published Paper

Inserted: 16 apr 2019
Last Updated: 4 mar 2020

Journal: Calc. Var. Partial Differential Equations
Volume: 59
Number: 56
Year: 2020

ArXiv: 1904.07028 PDF

Abstract:

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.