Open AccessCritical polyharmonic systems and optimal partitions
Author(s) -
Mónica Clapp,
Juan Carlos Aneiros Fernandez,
Alberto Saldaña
Publication year - 2021
Publication title -
communications on pure and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.077
H-Index - 42
eISSN - 1553-5258
pISSN - 1534-0392
DOI - 10.3934/cpaa.2021141
Subject(s) - disjoint sets , partition (number theory) , mathematics , limiting , combinatorics , invariant (physics) , discrete mathematics , mathematical physics , mechanical engineering , engineering
We establish the existence of solutions to a weakly-coupled competitive system of polyharmonic equations in \begin{document}$ \mathbb{R}^N $\end{document} which are invariant under a group of conformal diffeomorphisms, and study the behavior of least energy solutions as the coupling parameters tend to \begin{document}$ -\infty $\end{document} . We show that the supports of the limiting profiles of their components are pairwise disjoint smooth domains and solve a nonlinear optimal partition problem of \begin{document}$ \mathbb R^N $\end{document} . We give a detailed description of the shape of these domains.