L. O'Brien

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math.OC2026

On the structure of optimal free Dirichlet regions in mass transportation problems

Lucas D. O'Brien

For a compactly supported probability measure $I^¼$ on the $d$ -dimensional space $R^{d}$ , the average distance problem asks us to minimize the average distance functional ove…

math.OC2025

Structure of average distance minimizers in general dimensions

Lucas O'Brien, Forest Kobayashi, Young-Heon Kim

For a fixed, compactly supported probability measure $I^¼$ on the $d$ -dimensional space $R^{d}$ , we consider the problem of minimizing the $p^{th}$ -power average dis…