27 citations · 64 across the 26 of their papers we have counts for
33 papers
Optimal boundary regularity and a Hopf-type lemma for Dirichlet problems involving the logarithmic Laplacian
Víctor Hernández-Santamaría, Luis Fernando López Ríos, Alberto Saldaña
We study the optimal boundary regularity of solutions to Dirichlet problems involving the logarithmic Laplacian. Our proofs are based on the construction of suitable barriers via t…
A strong unique continuation property for weakly coupled elliptic systems
Mónica Clapp, Víctor Hernández-Santamaría, Alberto Saldaña
We establish the validity of a strong unique continuation property for weakly coupled elliptic systems, including competitive ones. Our proof exploits the system structure and uses…
Uniqueness and nondegeneracy of least-energy solutions to fractional Dirichlet problems
Abdelrazek Dieb, Isabella Ianni, Alberto Saldaña
We prove the uniqueness and nondegeneracy of least-energy solutions of a fractional Dirichlet semilinear problem in sufficiently large balls and in more general symmetric domains.…
Optimal pinwheel partitions for the Yamabe equation
Mónica Clapp, Jorge Faya, Alberto Saldaña
We establish the existence of an optimal partition for the Yamabe equation in the whole space made up of mutually linearly isometric sets, each of them invariant under the action o…
Configuration spaces and multiple positive solutions to a singularly perturbed elliptic system
Mónica Clapp, Alberto Saldaña, Andrzej Szulkin
We consider a weakly coupled singularly perturbed variational elliptic system in a bounded smooth domain with Dirichlet boundary conditions. We show that, in the competitive regime…
Exponential decay of the solutions to nonlinear Schrödinger systems
Felipe Angeles, Mónica Clapp, Alberto Saldaña
We show that the components of finite energy solutions to general nonlinear Schrödinger systems have exponential decay at infinity. Our results apply to positive or sign-changing c…
Small order limit of fractional Dirichlet sublinear-type problems
Felipe Angeles, Alberto Saldaña
We study the asymptotic behavior of solutions to various Dirichlet sublinear-type problems involving the fractional Laplacian when the fractional parameter s tends to zero. Dependi…
Existence of solutions to a slightly supercritical pure Neumann problem
Angela Pistoia, Alberto Saldaña, Hugo Tavares
We show the existence and multiplicity of concentrating solutions to a pure Neumann slightly supercritical problem in a ball. This is the first existence result for this kind of pr…
Classical solutions to integral equations with zero order kernels
Héctor A. Chang-Lara, Alberto Saldaña
We show global and interior higher-order log-Hölder regularity estimates for solutions of Dirichlet integral equations where the operator has a nonintegrable kernel with a singular…
Uniqueness and nondegeneracy for Dirichlet fractional problems in bounded domains via asymptotic methods
Abdelrazek Dieb, Isabella Ianni, Alberto Saldaña
We consider positive solutions of a fractional Lane-Emden type problem in a bounded domain with Dirichlet conditions. We show that uniqueness and nondegeneracy hold for the asympto…
Small order asymptotics for nonlinear fractional problems
Víctor Hernández-Santamaría, Alberto Saldaña
We study the limiting behavior of solutions to boundary value nonlinear problems involving the fractional Laplacian of order when the parameter tends to zero. In particula…
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…
Phase separation, optimal partitions, and nodal solutions to the Yamabe equation on the sphere
Mónica Clapp, Alberto Saldaña, Andrzej Szulkin
We study an optimal M-partition problem for the Yamabe equation on the round sphere, in the presence of some particular symmetries. We show that there is a correspondence between s…
A new look at the fractional Poisson problem via the Logarithmic Laplacian
Sven Jarohs, Alberto Saldana, Tobias Weth
We analyze the -dependence of solutions to the family of fractional Poisson problems in , on in an open bounded set…
Sharp asymptotic behavior of radial solutions of some planar semilinear elliptic problems
Isabella Ianni, Alberto Saldana
We consider the equation for any , either in or in the unit ball of centered at the origin with Dirichlet or Neumann…
Entire nodal solutions to the critical Lane-Emden system
Mónica Clapp, Alberto Saldaña
We establish the existence of finitely many sign-changing solutions to the Lane-Emden system whe…
On fractional higher-order Dirichlet boundary value problems: between the Laplacian and the bilaplacian
Alberto Saldaña
The solutions of boundary value problems for the Laplacian and the bilaplacian exhibit very different qualitative behaviors. Particularly, the failure of general maximum principles…
Sharp concentration estimates near criticality for radial sign-changing solutions of Dirichlet and Neumann problems
Massimo Grossi, Alberto Saldaña, Hugo Tavares
We consider radial solutions of the slightly subcritical problem either on () or…
Positive powers of the Laplacian in the half-space under Dirichlet boundary conditions
Nicola Abatangelo, Serena Dipierro, Mouhamed Moustapha Fall +2
We present explicit formulas for solutions to nonhomogeneous boundary value problems involving any positive power of the Laplacian in the half-space. For non-integer powers the ope…