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arXiv · 2510.03794

Gamma Convergence of Partially Segregated Elliptic Systems

Farid Bozorgnia·Avetik Arakelyan
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Abstract

We study partially segregated elliptic systems through the use of penalized energy functionals. These systems arise from the minimization of Gross-Pitaevskii-type energies that capture the behavior of multi-component ultracold gas mixtures and other systems involving multiple interacting fluid or gas species. In the case when the domain is planar, i.e., in $\mathbb{R}^2$, our main result is the Gamma convergence of penalized energy to the constrained Dirichlet energy with strict segregation. The proof combines lower semicontinuity arguments with a recovery sequence construction based on geometric decompositions near interfaces and triple junctions. This establishes a rigorous variational link between the penalized and constrained formulations.

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Farid Bozorgnia, Avetik Arakelyan. 2025-10-04. Gamma Convergence of Partially Segregated Elliptic Systems. https://arxiv.org/abs/2510.03794

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