Related papers: Self-similar minimizers of a branched transport fu…
We consider a branched transport problem with weakly imposed boundary conditions. This problem arises as a reduced model for pattern formation in type-I superconductors. For this model, it is conjectured that the dimension of the boundary…
Based on the multidimensional irreducible paving of De March & Touzi, we provide a multi-dimensional version of the quasi sure duality for the martingale optimal transport problem, thus extending the result of Beiglb\"ock, Nutz & Touzi.…
We consider a branched transport type problem which describes the magnetic flux through type-I superconductors in a regime of very weak applied fields. At the boundary of the sample, deviation of the magnetization from being uniform is…
We introduce and investigate properties of a variant of the semi-discrete optimal transport problem. In this problem, one is given an absolutely continuous source measure and cost function, along with a finite set which will be the support…
We study those measures whose doubling constant is the least possible among doubling measures on a given metric space. It is shown that such measures exist on every metric space supporting at least one doubling measure. In addition, a…
We prove a geometric linearisation result for minimisers of optimal transport problems where the cost-function is strongly p-convex and of p-growth. Initial and target measures are allowed to be rough, but are assumed to be close to…
A prominent model for transportation networks is branched transport, which seeks the optimal transportation scheme to move material from a given initial to a final distribution. The cost of the scheme encodes a higher transport efficiency…
We propose a new anisotropic optimal transport model based on the theory of currents, where the anisotropic cost function splits as the product of a factor depending only on the spatial direction and a factor depending only on the…
We prove that for the generic boundary, in the sense of Baire categories, there exists a unique minimizer of the associated optimal branched transportation problem.
We consider an optimal transportation problem with more than two marginals. We use a family of semi-Riemannian metrics derived from the mixed, second order partial derivatives of the cost function to provide upper bounds for the dimension…
We study minimizers of non-autonomous energies with minimal growth and coercivity assumptions on the energy. We show that the minimizer is nevertheless the solution of the relevant Euler--Lagrange equation or inequality. The main tool is an…
We investigate the small regularization limit of entropic optimal transport when the cost function is the Euclidean distance in dimensions $d > 1$, and the marginal measures are absolutely continuous with respect to the Lebesgue measure.…
We study the problem of transporting one probability measure to another via an autonomous velocity field. We rely on tools from the theory of optimal transport. In one space-dimension, we solve a linear homogeneous functional equation to…
We consider so-called branched transport and variants thereof in two space dimensions. In these models one seeks an optimal transportation network for a given mass transportation task. In two space dimensions, they are closely connected to…
In this paper we consider the branched transportation problem in 2D associated with a cost per unit length of the form $1 + \alpha m$ where $m$ denotes the amount of transported mass and $\alpha > 0$ is a fixed parameter (notice that the…
We prove that minimal Dirac operators on the half-line are self-modeling, which means that such an operator is determined by its arbitrary unitary copy uniquely up to a transformation (shape equivalence) which changes its potential by a…
Given a complete doubling metric measure space $X$ that supports a $2$-Poincar\'e inequality, we approximate harmonic functions on a bounded domain $\Omega$ with a prescribed Newton-Sobolev boundary data. Our approach is based on the…
First we present two classical models of Branched Transport: the Lagrangian model introduced by Bernot, Caselles, Morel, Maddalena, Solimini, and the Eulerian model introduced by Xia. An emphasis is put on the Lagrangian model, for which we…
The paper analyzes a mollification algorithm, for the numerical computation of optimal irrigation patterns. This provides a regularization of the standard irrigation cost functional, in a Lagrangian framework. Lower semicontinuity and…
This paper is devoted to variational problems on the set of probability measures which involve optimal transport between unequal dimensional spaces. In particular, we study the minimization of a functional consisting of the sum of a term…