2025/10/04 by Bozorgnia, Farid, Arakelyan, Avetik
#35J50 #35R35 #49J45 #49Q05 #Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.2510.03794
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 ℝ2, 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.