15 citations · 15 across the 3 of their papers we have counts for
5 papers
The Poisson equation from non-local to local
Umberto Biccari, Víctor Hernández-Santamaría
We analyze the limit behavior as of the solution to the fractional Poisson equation , with homogeneous Dirichlet boundary conditions $u_s\equiv 0…
A Finite Element approximation of the one-dimensional fractional Poisson equation with applications to numerical control
Umberto Biccari, Víctor Hernández-Santamaría
We present a finite element (FE) scheme for the numerical approximation of the solution to a non-local Poisson equation involving the one-dimensional fractional Laplacian $(-d_x^2)…
Local elliptic regularity for the Dirichlet fractional Laplacian
Umberto Biccari, Mahamadi Warma, Enrique Zuazua
We analyze the local elliptic regularity of weak solutions to the Dirichlet problem associated with the fractional Laplacian on an arbitrary bounded open set $Ω\subset\mat…
Local regularity for fractional heat equations
Umberto Biccari, Mahamadi Warma, Enrique Zuazua
We prove the maximal local regularity of weak solutions to the parabolic problem associated with the fractional Laplacian with homogeneous Dirichlet boundary conditions on an arbit…
Null controllability for a heat equation with a singular inverse-square potential involving the distance to the boundary function
Umberto Biccari, Enrique Zuazua
This article is devoted to the analysis of control properties for a heat equation with singular potential , defined on a bounded domain , where $…