Phase field models for two-dimensional branched transportation problems

Benedikt Wirth

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arXiv · 1805.05141

Phase field models for two-dimensional branched transportation problems

Benedikt Wirth

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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.

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Benedikt Wirth. 2018-05-14. Phase field models for two-dimensional branched transportation problems. https://arxiv.org/abs/1805.05141

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