arXiv subjects

Martijn Zaal

Publications and source records attributed to Martijn Zaal.

2 recordsLinked to original sources

arXiv2015

On the Role of Cylindrical Functions in Kantorovich duality

We study the dual formulation of the Monge-Kantorovich optimal transportation problem, in particular under what circumstances it is permitted in an infinite dimensional setting to use cylindrical functions, i.e. functions of the form $φ\circ P$ where $P$ is a finite-rank operator and $φ$ is a smooth, compactly supported function. In the last section, some examples of applications are presented.

math.FA↗

arXiv2012

Cell Swelling by Osmosis: a Variational Approach

A very simple model for cell swelling by osmosis is introduced, resulting in a parabolic free boundary problem. In case of radially symmetric initial conditions, it is shown that the model can be viewed as a gradient flow involving entropy, surface area and the Wasserstein metric. This observation is used to construct solutions and explain the presence and nature of osmosis.

math.DS↗