20 papers · 1 filter
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…
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…