3 papers
math.OC2026
On the structure of optimal free Dirichlet regions in mass transportation problems
Lucas D. O'Brien
For a compactly supported probability measure on the -dimensional space , the average distance problem asks us to minimize the average distance functional ove…
math.AP2026
On the Hausdorff dimension and singularities of the monopolist's free boundary curve
Robert J. McCann, Lucas D. O'Brien, Cale Rankin
The simplest genuinely multidimensional monopolist's problem involves minimizing a linearly perturbed Dirichlet energy among nonnegative convex functions on an open domain $X \…
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 on the -dimensional space , we consider the problem of minimizing the -power average dis…