Phase field models for two-dimensional branched transportation problems
Optimization and Control
2018-05-15 v1
Abstract
We analyse the following inverse problem. Given a nonconvex functional (from a specific, but quite general class) of normal, codimension-1 currents (which in two spatial dimensions can be interpreted as transportation networks), find the potential of a phase field energy which approximates the given functional. We prove existence of a solution as well as its characterization via a linear deconvolution problem. We also provide an explicit formula that allows to approximate the solution arbitrarily well in the supremum norm.
Cite
@article{arxiv.1805.05141,
title = {Phase field models for two-dimensional branched transportation problems},
author = {Benedikt Wirth},
journal= {arXiv preprint arXiv:1805.05141},
year = {2018}
}