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math.AP2026
Monopolist nonlinear pricing in a seller's market
Lucas D. O'Brien
In this paper, we study the Rochet-Choné model of monopolist pricing in the seller's market limit. We introduce a monotonicity formula which yields an asymptotic description of sol…
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 over…
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 \…