5 papers
Besov regularity of solutions to the Dirichlet problem for the Bessel -Laplacian
Juan Pablo Borthagaray, Leandro M. Del Pezzo, José Camilo Rueda Niño
We study the Dirichlet problem for a class of fractional -Laplacian operators of order defined through the Riesz fractional gradient, which differs fundamentally f…
A mixed formulation for the fractional Poisson problem
Juan Pablo Borthagaray, Nahuel de León
The mixed formulation of the classical Poisson problem introduces the flux as an additional variable, leading to a system of coupled equations. Using fractional calculus identities…
A deep first-order system least squares method for the obstacle problem
Gabriel Acosta, Eugenia Belén, Francisco M. Bersetche +1
We propose a deep learning approach to the obstacle problem inspired by the first-order system least-squares (FOSLS) framework. This method reformulates the problem as a convex min…
On some coupled local and nonlocal diffusion models
Juan Pablo Borthagaray, Patrick Ciarlet
We study problems in which a local model is coupled with a nonlocal one. We propose two energies: both of them are based on the same classical weighted -semi norm to model the…
Monotone two-scale methods for a class of integrodifferential operators and applications
Juan Pablo Borthagaray, Ricardo H. Nochetto, Abner J. Salgado +1
We develop a monotone, two-scale discretization for a class of integrodifferential operators of order , . We apply it to develop numerical schemes, and derive poin…