# Riesz-type inequalities and overdetermined problems for triangles and quadrilaterals

@inproceedings{Bonacini2021RiesztypeIA, title={Riesz-type inequalities and overdetermined problems for triangles and quadrilaterals}, author={M. Bonacini and R. Cristoferi and I. Topaloglu}, year={2021} }

We consider Riesz-type nonlocal interaction energies over convex polygons. We prove the analog of the Riesz inequality in this discrete setting for triangles and quadrilaterals, and obtain that among all N-gons with fixed area, the nonlocal energy is maximized by a regular polygon, for N = 3, 4. Further we derive necessary first-order stationarity conditions for a polygon with respect to a restricted class of variations, which will then be used to characterize regular N-gons, for N = 3, 4, as… Expand

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