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Critical polyharmonic systems and optimal partitions

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    * Corresponding author 
M. Clapp was supported by CONACYT grant A1-S-10457 (Mexico), J.C. Fernández was supported by a CONACYT postdoctoral fellowship (Mexico), and A. Saldaña was supported by UNAM-DGAPA-PAPIIT grant IA101721 (Mexico)
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  • We establish the existence of solutions to a weakly-coupled competitive system of polyharmonic equations in $ \mathbb{R}^N $ which are invariant under a group of conformal diffeomorphisms, and study the behavior of least energy solutions as the coupling parameters tend to $ -\infty $. We show that the supports of the limiting profiles of their components are pairwise disjoint smooth domains and solve a nonlinear optimal partition problem of $ \mathbb R^N $. We give a detailed description of the shape of these domains.

    Mathematics Subject Classification: Primary: 35G50; Secondary: 35G30, 35B06, 58J70, 35B33.


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