The generalized Favard problem
The paper deals with a geometrical optimization problem for isoperimetric plane sets contained in a circular sector. For a complete circle, this problem was solved by J. M. Favard in 1929. This geometrical optimization problem is formulated as a problem of optimal control where the control appears as a distribution. With the help of Pontryagin's maximum principle necessary optimality conditions are investigated. Finally, the generalized Favard problem is solved and it is shown that the optimal figure is an almost regular inpolyeder of a sector.
scientific article; zbMATH DE number 821689