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arXiv · 2606.29906

On the existence of canonical multi-phase free boundary Brakke flows: a case study

Alessandro Scapin
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Abstract

We establish the global-in-time existence of a codimension $1$ canonical multi-phase free boundary Brakke flow in the upper halfspace which is integer rectifiable up boundary, starting from a countably $n$-rectifiable set. Under a suitable uniform density ratio assumption on the initial datum, we show that the free boundary carries no positive mass for some short time.

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Alessandro Scapin. 2026-06-29. On the existence of canonical multi-phase free boundary Brakke flows: a case study. https://arxiv.org/abs/2606.29906

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