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.
Euler’s optimal profile problem
Mainini, Edoardo;Percivale, Danilo
2020-01-01
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.
File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
Euler journal.pdf
accesso aperto
Descrizione: Articolo su rivista
Tipologia:
Documento in Post-print
Dimensione
728.34 kB
Formato
Adobe PDF
|
728.34 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
