PreprintCC BY 4.0arXiv
Triple Junctions in Multi-Phase Obstacle type Problems
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):= ∫B1 (1/2 |∇ U|2 + F · U)dx among all competitors U=(u1,…, uN) with non-negative components ui ≥ 0 with disjoint supports, and constant forcing terms fi>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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BibTeX
@misc{silva2026triple,
title = {{Triple Junctions in Multi-Phase Obstacle type Problems}},
author = {Daniela De Silva and Ovidiu Savin and Henrik Shahgholian},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18270},
eprint = {2610.18270},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18270},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Triple Junctions in Multi-Phase Obstacle type Problems
AU - Daniela De Silva
AU - Ovidiu Savin
AU - Henrik Shahgholian
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18270
UR - https://arxiv.org/abs/2610.18270
AB - 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):= ∫_B_1 (1/2 |∇ U|^2 + F · U)dx among all competitors U=(u^1,…, u^N) with non-negative components u^i ≥ 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).
ER -