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math.AP2021★ 1 cited
Area quasi-minimizing partitions with a graphical constraint: relaxation and two-dimensional partial regularity
Marco Bonacini, Riccardo Cristoferi
We consider a variational model for periodic partitions of the upper half-space into three regions, where two of them have prescribed volume and are subject to the geometrical cons…
math.AP2021★ 4 cited
Riesz-type inequalities and overdetermined problems for triangles and quadrilaterals
Marco Bonacini, Riccardo Cristoferi, Ihsan Topaloglu
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 obtai…