145 citations · 506 across the 57 of their papers we have counts for
8 papers · 1 filter
Self-improving properties for a class of elliptic and parabolic equations on bounded domains
Tadele Mengesha, Abner J. Salgado
We discuss self improving properties of some local and nonlocal, elliptic and parabolic, equations on bounded domains. We employ a functional analytic approach wherein the solution…
Analysis and approximation of elliptic problems with Uhlenbeck structure in convex polytopes
Tadele Mengesha, Enrique Otarola, Abner J. Salgado
We prove the well posedness in weighted Sobolev spaces of certain linear and nonlinear elliptic boundary value problems posed on convex domains and under singular forcing. It is as…
Time fractional gradient flows: Theory and numerics
Wenbo Li, Abner J. Salgado
We develop the theory of fractional gradient flows: an evolution aimed at the minimization of a convex, l.s.c.~energy, with memory effects. This memory is characterized by the fact…
The Darcy problem with porosity depending exponentially on the pressure
Zerihun Kinfe Birhanu, Tadele Mengesha, Abner J. Salgado
We consider the flow of a viscous incompressible fluid through a porous medium. We allow the permeability of the medium to depend exponentially on the pressure and provide an analy…
Estimation of the continuity constants for Bogovski\uı and regularized Poincaré integral operators
Johnny Guzman, Abner J. Salgado
We study the dependence of the continuity constants for the regularized Poincaré and Bogovski\uı integral operators acting on differential forms defined on a domain of $\mathbb…
The Poisson and Stokes problems in nonconvex, Lipschitz polytopes
Enrique Otarola, Abner J. Salgado
We show the well-posedness of the Poisson and Stokes problems in weighted spaces over nonconvex, Lipschitz polytopes. For a particular range of , we consider those weights in th…