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- W3133909049 abstract "We consider Riesz-type nonlocal interaction energies over 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 solutions to an overdetermined free boundary problem." @default.
- W3133909049 created "2021-03-15" @default.
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- W3133909049 date "2022-01-04" @default.
- W3133909049 modified "2023-10-07" @default.
- W3133909049 title "Riesz-type Inequalities and Overdetermined Problems for Triangles and Quadrilaterals" @default.
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- W3133909049 doi "https://doi.org/10.1007/s12220-021-00737-7" @default.
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