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On some singularly perturbed elliptic systems modeling partial segregation: uniform H\"older estimates and basic properties of the limits

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arxiv 2409.11976 v2 pith:YGT26KTT submitted 2024-09-18 math.AP

classification math.AP
keywords systemsellipticestimatesfeaturegasesinteractionslimitingmodeling
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We prove uniform H\"older estimates in a class of singularly perturbed competition-diffusion elliptic systems, with the particular feature that the interactions between the components occur three by three (ternary interactions). These systems are associated to the minimization of Gross-Pitaevski energies modeling ternary mixture of ultracold gases and other multicomponent liquids and gases. We address the question whether this regularity holds uniformly throughout the approximation process up to the limiting profiles, answering positively. A very relevant feature of limiting profiles in this process is that they are only partially segregated, giving rise to new phenomena of geometric pattern formation and optimal regularity.

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Cited by 2 Pith papers

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  1. Structure of the free interfaces near triple junction singularities in harmonic maps and optimal partition problems

    math.AP 2024-12 conditional novelty 8.0 of 10

    Energy-minimizing maps into trees have, near every frequency-3/2 point, free interfaces composed of three C^{1,α} surfaces meeting at 120 degrees along a C^{1,α} (d-2)-dimensional boundary.

  2. On least energy solutions for a nonlinear Schr\"odinger system with $K$-wise interaction

    math.AP 2025-07 conditional novelty 7.0 of 10

    For K-wise coupled nonlinear Schrödinger systems, the authors prove a sharp β-threshold separating semi-trivial from fully non-trivial ground states, and show that as β → -∞ only two components fully segregate while t...

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