From the 1 of 9 linked papers with an AI index.
9 papers
Self-improving properties for a class of elliptic and parabolic equations on bounded domains
Tadele Mengesha, Abner J. Salgado
The paper studies how solutions to certain local and nonlocal elliptic and parabolic equations on bounded domains gain extra regularity, using interpolation theory and analytic per…
Analysis and approximation of a two-dimensional induction heating problem
Gabriel R. Barrenechea, Katherine MacKenzie, Abner Salgado
In this paper, we analyse the existence of solutions and finite element approximation of a steady-state two-dimensional induction heating problem. One of the main difficulties of t…
A pointwise tracking optimal control problem for a fractional, semilinear PDE
Enrique Otarola, Abner J. Salgado
We analyze an optimal control problem with pointwise tracking for a fractional semilinear elliptic partial differential equation. The diffusion is characterized by the spectral fra…
Approximation of higher-order powers of the spectral fractional Laplacian via polyharmonic extension
Enrique Otárola, Abner J. Salgado
We use the polyharmonic extension approach to develop a numerical technique for discretizing higher-order powers of the spectral fractional Laplacian with .
The spectral fractional Laplacian with measure valued right hand sides: analysis and approximation
Enrique Otarola, Abner J. Salgado
We consider the spectral definition of the fractional Laplace operator and study a basic linear problem involving this operator and singular forcing. In two dimensions, we introduc…
A perturbed preconditioned gradient descent method for the unconstrained minimization of composite objectives
Jea-Hyun Park, Abner J. Salgado, Steven M. Wise
We introduce a perturbed preconditioned gradient descent (PPGD) method for the unconstrained minimization of a strongly convex objective with a locally Lipschitz continuous gra…