Critical polyharmonic systems and optimal partitions

2021/05/08 by Clapp, Mónica, Fernández, Juan Carlos, Saldaña, Alberto · 1 citation
#35B06 #35B33 #35G30 #35G50 #58J70 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2105.03754

Abstract

We establish the existence of solutions to a weakly-coupled competitive system of polyharmonic equations in 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 -∞. 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 R^N. We give a detailed description of the shape of these domains.

Cited by

• The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces

Related

• Construction of solutions for the critical polyharmonic equation with competing potentials
• Existence of polyharmonic maps in critical dimensions
• Yamabe systems and optimal partitions on manifolds with symmetries
• Fractional Q-curvature on the sphere and optimal partitions
• New type of solutions for the critical polyharmonic equation