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Creators/Authors contains: "Bonacini, Marco"

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  1. ; (, Interfaces and Free Boundaries, Mathematical Analysis, Computation and Applications)
    We consider perimeter perturbations of a class of attractive-repulsive energies, given by the sum of two nonlocal interactions with power-law kernels, defined over sets with fixed measure. We prove that there exist curves in the perturbation-volume parameter space that separate stability/instability and global minimality/nonminimality regions of the ball, and provide a precise description of these curves for certain interaction kernels. In particular, we show that in small perturbation regimes there are (at least) two disconnected regions for the mass parameter in which the ball is stable, separated by an instability region. 
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    Free, publicly-accessible full text available June 6, 2026
  2. ; ; (, The American Mathematical Monthly)
    Free, publicly-accessible full text available June 9, 2026
  3. ; ; (, Proceedings of the Royal Society of Edinburgh: Section A Mathematics)
    Recently it has been shown that the unique local perimeter minimizing partitioning of the plane into three regions, where one region has finite area and the other two have infinite measure, is given by the so-called standard lens partition. Here we prove a sharp stability inequality for the standard lens, hence strengthening the local minimality of the lens partition in a quantitative form. As an application of this stability result we consider a nonlocal perturbation of an isoperimetric problem. 
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    Free, publicly-accessible full text available January 27, 2026