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Cited article:

A solution to Newton’s least resistance problem is uniquely defined by its singular set

Alexander Plakhov
Calculus of Variations and Partial Differential Equations 61 (5) (2022)
https://doi.org/10.1007/s00526-022-02300-w

Euler’s optimal profile problem

Francesco Maddalena, Edoardo Mainini and Danilo Percivale
Calculus of Variations and Partial Differential Equations 59 (2) (2020)
https://doi.org/10.1007/s00526-020-1707-9