15 papers
Critical polyharmonic systems and optimal partitions
Mónica Clapp, Juan Carlos Fernández, Alberto Saldaña
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…
Symmetry properties of sign-changing solutions to nonlinear parabolic equations in unbounded domains
Juraj Földes, Alberto Saldaña, Tobias Weth
We study the asymptotic (in time) behavior of positive and sign-changing solutions to nonlinear parabolic problems in the whole space or in the exterior of a ball with Dirichlet bo…
Existence and convergence of solutions to fractional pure critical exponent problems
Víctor Hernández-Santamaría, Alberto Saldaña
We study existence and convergence properties of least-energy symmetric solutions (l.e.s.s.) to the pure critical problem \begin{equation*} (-Δ)^su_s=|u_s|^{2^\star_s-2}u_s, \quad…
On the least-energy solutions of the pure Neumann Lane-Emden equation
Alberto Saldaña, Hugo Tavares
We study the pure Neumann Lane-Emden problem in a bounded domain \[ -Δu = |u|^{p-1} u \text{ in }Ω, \qquad \partial_νu=0 \text{ on }\partial Ω, \] in the subcritical, critical, and…
A solution to a slightly subcritical elliptic problem with non-power nonlinearity
Monica Clapp, Rosa Pardo, Angela Pistoia +1
We consider a slightly subcritical Dirichlet problem with a non-power nonlinearity in a bounded smooth domain. For this problem, standard compact embeddings cannot be used to guara…
Fractional Laplacians on ellipsoids
Nicola Abatangelo, Sven Jarohs, Alberto Saldaña
We show explicit formulas for the evaluation of (possibly higher-order) fractional Laplacians of some functions supported on ellipsoids. In particular, we derive the explicit expre…