[DSRP Evidence](https://dsrpevidence.org/)

# Structure of the Free Interfaces Near Triple Junction Singularities in Harmonic Maps and Optimal Partition Problems

Ognibene and Velichkov, 2026, Archive for Rational Mechanics and Analysis — Mathematics

Patterns: [Distinctions](https://dsrpevidence.org/pattern/distinctions), [Systems](https://dsrpevidence.org/pattern/systems)

## In short

The theorem characterizes how a domain's whole free-interface structure is built from distinct constituent surface-parts meeting at a precisely characterized shared boundary, a system of parts governed by a rigorous distinction.

## What they found (results)

The paper proves that near frequency-3/2 triple-junction points of energy-minimizing harmonic maps into trees, the free interface decomposes into exactly three smooth (d-1)-dimensional surfaces meeting along a common regular boundary at 120-degree angles, a result that also applies to optimal spectral partition problems.

These researchers were not testing DSRP. The finding is theirs; the correspondence to DSRP is drawn by this site.

[Source](https://doi.org/10.1007/s00205-026-02221-4)