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.
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Acknowledgements
The authors are members of the GNAMPA group of the Istituto Nazionale di Alta Matematica (INdAM).
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Communicated by C. de Lellis.
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