no. 2
An example of non-convex minimization and an application to Newton's problem of the body of least resistance
Annales de l'I.H.P. Analyse non linéaire, Tome 18 (2001) no. 2, pp. 179-198 
@article{AIHPC_2001__18_2_179_0,
     author = {Lachand-Robert, T. and Peletier, M. A.},
     title = {An example of non-convex minimization and an application to {Newton's} problem of the body of least resistance},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {179--198},
     year = {2001},
     publisher = {Elsevier},
     volume = {18},
     number = {2},
     mrnumber = {1808028},
     zbl = {0993.49002},
     language = {en},
     url = {https://www.numdam.org/item/AIHPC_2001__18_2_179_0/}
}
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Lachand-Robert, T.; Peletier, M. A. An example of non-convex minimization and an application to Newton's problem of the body of least resistance. Annales de l'I.H.P. Analyse non linéaire, Tome 18 (2001) no. 2, pp. 179-198. https://www.numdam.org/item/AIHPC_2001__18_2_179_0/

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