The derivative at zero of the conformal fractional Laplacian yields a conformal logarithmic Laplacian whose spectral, stereographic, and Yamabe-type properties are characterized, including an explicit classification of nonnegative weak solutions.
Fractional $Q$-curvature on the sphere and optimal partitions
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We study an optimal partition problem on the sphere, where the cost functional is associated with the fractional $Q$-curvature in terms of the conformal fractional Laplacian on the sphere. By leveraging symmetries, we prove the existence of a symmetric minimal partition through a variational approach. A key ingredient in our analysis is a new H\"older regularity result for symmetric functions in a fractional Sobolev space on the sphere. As a byproduct, we establish the existence of infinitely many solutions to a nonlocal weakly-coupled competitive system on the sphere that remain invariant under a group of conformal diffeomorphisms and we investigate the asymptotic behavior of least-energy solutions as the coupling parameters approach negative infinity.
citation-role summary
background 1
citation-polarity summary
fields
math.AP 1years
2025 1verdicts
CONDITIONAL 1roles
background 1polarities
unclear 1representative citing papers
citing papers explorer
-
The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces
The derivative at zero of the conformal fractional Laplacian yields a conformal logarithmic Laplacian whose spectral, stereographic, and Yamabe-type properties are characterized, including an explicit classification of nonnegative weak solutions.