Optimal sets for a class of minimization problems with convex constraints

Details Optimal sets for a class of minimization problems with convex constraints Optimal sets for a class of minimization problems with convex constraints

2010-12-21

arxiv.org/abs/1012.4666v1

Mathematics

Analysis of PDEs

Scientific paper

We look for the minimizers of the functional $\jla{\la}(\oo)=\la|\oo|-P(\oo)$ among planar convex domains constrained to lie into a given ring. We prove that, according to the values of the parameter $\la$, the solutions are either a disc or a polygon. In this last case, we describe completely the polygonal solutions by reducing the problem to a finite dimensional optimization problem. We recover classical inequalities for convex sets involving area, perimeter and inradius or circumradius and find a new one.

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