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arXiv · 2610.18270

Triple Junctions in Multi-Phase Obstacle type Problems

Daniela De Silva·Ovidiu Savin·Henrik Shahgholian
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Abstract

We study the regularity of the free boundary for a multi-phase obstacle-type problem associated to quadrature domains, which arises from the minimization of the energy $$J(U,F):= \int_{B_1} (\frac 1 2 |\nabla U|^2 + F \cdot U)dx$$ among all competitors $U=(u^1,\ldots, u^N)$ with non-negative components $u^i \geq 0$ with disjoint supports, and constant forcing terms $f^i>0.$ We focus on the geometry of the free boundary at points where at least three distinct components meet (triple junctions).

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Daniela De Silva, Ovidiu Savin, Henrik Shahgholian. 2026-10-13. Triple Junctions in Multi-Phase Obstacle type Problems. https://arxiv.org/abs/2610.18270

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