Related papers: An exterior optimal transport problem

In this paper we study the three-marginal optimal mass transportation problem for the Coulomb cost on the plane $\R^2$. The key question is the optimality of the so-called Seidl map, first disproved by Colombo and Stra. We generalize the…

We extend a dimensional upper bound on how much an optimal transport map can degenerate for the quadratic transportation cost, originally due to Caffarelli, to cost functions that satisfy the curvature condition of Ma, Trudinger, and Wang.

Let $X$ and $Y$ be domains of $\mathbb{R}^n$ equipped with respective probability measures $\mu$ and $ \nu$. We consider the problem of optimal transport from $\mu$ to $\nu$ with respect to a cost function $c: X \times Y \to \mathbb{R}$. To…

We investigate the optimal mass transport problem associated to the following "ballistic" cost functional on phase space $M\times M^*$, $$ b_T(v, x):=\inf\{\langle v, \gamma (0)\rangle +\int_0^TL(\gamma (t), {\dot \gamma}(t))\, dt, \gamma…

In this paper, we study the optimal transportation for generalized Lagrangian $L=L(x, u,t)$, and consider the cost function as following: $$c(x, y)=\inf_{\substack{x(0)=x\\x(1)=y\\u\in\mathcal{U}}}\int_0^1L(x(s), u(x(s),s), s)ds.$$ Where…

Encouraged by the study of extremal limits for sums of the form $$\lim_{N\to\infty}\frac{1 }{N}\sum_{n=1}^N c(x_n,y_n)$$ with uniformly distributed sequences $\{x_n\},\,\{y_n\}$ the following extremal problem is of interest…

For a family of probability spaces $\{(X_k,\mathcal{B}_{X_k},\mu_k)\}_{k=1}^N$ and a cost function $c: X_1\times\cdots\times X_N\to \mathbb{R}$ we consider the Monge-Kantorovich problem \begin{align*}\tag{MK}\label{MONKANT}…

Consider a transportation problem with sets of sources and sinks. There are profits and prices on the edges. The goal is to maximize the profit while meeting the following constraints; the total flow going out of a source must not exceed…

For a finite metric graph $X=(V,E,\ell)$, where $V$ is endowed with the shortest path metric, we consider the transportation cost problem associated with the distance $d$ on $V$. Namely, for $f$ a function with total sum 0 on $V$, write…

We consider the optimal transportation problem on a globally hyperbolic spacetime with a cost function $c$, which corresponds to the optimal transportation problem on a complete Riemannian manifold where the cost function is given by the…

The Monge-Kantorovich transportation problem involves optimizing with respect to a given a cost function. Uniqueness is a fundamental open question about which little is known when the cost function is smooth and the landscapes containing…

We introduce and study a multi-marginal optimal partial transport problem. Under a natural and sharp condition on the dominating marginals, we establish uniqueness of the optimal plan. Our strategy of proof establishes and exploits a…

This work establishes that an optimal transport~(OT) problem regularized by a given $f$-divergence admits the same solution as another OT problem regularized by a different $g$-divergence, under an appropriate transformation of the cost…

We study Monge's optimal transportation problem, where the cost is given by optimal control cost. We prove the existence and uniqueness of an optimal map under certain regularity conditions on the Lagrangian, absolute continuity of the…

A fundamental concept in optimal transport is c-cyclical monotonicity: it allows to link the optimality of transport plans to the geometry of their support sets. Recently, related concepts have been successfully applied in the…

In this paper, we prove existence of $L^p$-optimal transport maps with $p \in (1,\infty)$ in a class of branching metric spaces defined on $\mathbb{R}^N$. In particular, we introduce the notion of cylinder-like convex function and we prove…

Optimal transportation with capacity constraints, a variant of the well-known optimal transportation problem, is concerned with transporting one probability density $f \in L^1(\mathbb{R}^m)$ onto another one $g \in L^1(\mathbb{R}^n)$ so as…

A key inequality which underpins the regularity theory of optimal transport for costs satisfying the Ma--Trudinger--Wang condition is the Pogorelov second derivative bound. This translates to an apriori interior $C^1$ estimate for smooth…

In the optimal partial transport problem, one is asked to transport a fraction $0<m \leq \min\{||f||_{L^1}, ||g||_{L^1}\}$ of the mass of $f=f \chi_\Omega$ onto $g=g\chi_\Lambda$ while minimizing a transportation cost. If $f$ and $g$ are…

Continuity of the value of the martingale optimal transport problem on the real line w.r.t. its marginals was recently established in Backhoff-Veraguas and Pammer [2] and Wiesel [21]. We present a new perspective of this result using the…