Riesz-type inequalities and overdetermined problems for triangles and quadrilaterals

Autor:	Marco Bonacini, Riccardo Cristoferi, Ihsan Topaloglu
Rok vydání:	2021
Předmět:	Mathematics - Analysis of PDEs Optimization and Control (math.OC) Astronomy FOS: Mathematics Geometry and Topology Computer Science::Computational Geometry 35N25 49Q10 49Q20 49J10 49J40 49K21 Mathematics - Optimization and Control Mathematics Analysis of PDEs (math.AP)
Zdroj:	The Journal of Geometric Analysis, 32, 1-31 The Journal of Geometric Analysis, 32, 2, pp. 1-31
ISSN:	1050-6926
DOI:	10.48550/arxiv.2103.06657
Popis:	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. Comment: This is a post-peer-review, pre-copyedit version of an article that will appear in the Journal of Geometric Analysis. The final authenticated version is available online at: https://doi.org/10.1007/s12220-021-00737-7
Databáze:	OpenAIRE
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