Gamma Convergence of Partially Segregated Elliptic Systems
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909825408958464 |
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| author | Bozorgnia, Farid Arakelyan, Avetik |
| author_facet | Bozorgnia, Farid Arakelyan, Avetik |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_03794 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gamma Convergence of Partially Segregated Elliptic Systems Bozorgnia, Farid Arakelyan, Avetik Analysis of PDEs 35J50, 49J45, 35R35, 49Q05 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. |
| title | Gamma Convergence of Partially Segregated Elliptic Systems |
| topic | Analysis of PDEs 35J50, 49J45, 35R35, 49Q05 |
| url | https://arxiv.org/abs/2510.03794 |