4 papers
Positive and nodal limiting profiles for a semilinear elliptic equation with a shrinking region of attraction
Mónica Clapp, Víctor Hernández-Santamaría, Alberto Saldaña
We study the existence and concentration of positive and nodal solutions to a Schrödinger equation in the presence of a shrinking self-focusing core of arbitrary shape. Via a suita…
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…
FEM for 1D-problems involving the logarithmic Laplacian: error estimates and numerical implementation
Víctor Hernández-Santamaría, Sven Jarohs, Alberto Saldaña +1
We present the numerical analysis of a finite element method (FEM) for one-dimensional Dirichlet problems involving the logarithmic Laplacian (the pseudo-differential operator that…