5 papers · 1 filter
Qualitative-to-quantitative regularity for degenerate equations
Aelson Sobral, Eduardo V. Teixeira, José Miguel Urbano
We establish a principle that converts qualitative regularity into uniform interior estimates for degenerate equations. For the -Laplace equation, , we prove that local $C^…
The Monge--Ampère equation on graphs
Ahmed Alkhozaae, Julio D. Rossi, Aelson Sobral +1
We introduce a version of the Monge--Ampère equation on finite graphs, motivated by nonlinear graph-based interpolation and semi-supervised learning. The operator is defined as the…
Lipschitz regularity for the parabolic obstacle problem
David Jesus, Aelson Sobral, José Miguel Urbano
We study the obstacle problem for the parabolic fractional Laplace equation \[\partial_t u+(-Δ_p)^su = 0\] in the degenerate range . We prove that viscosity soluti…
A coupled prediction-correction Hughes' model for congested crowd motion
Hamza Ennaji, Noureddine Igbida, Ghadir Jradi +1
In this work, we introduce a new macroscopic model for crowd motion inspired by the celebrated Hughes' model \cite{Hughes2002, Hughes2003}, which couples a nonlinear conservation l…
A granular model for crowd motion and pedestrian flow
Noureddine Igbida, José Miguel Urbano
We study a granular model for congested crowd motion and pedestrian flow. Our approach is based on an approximation through a Hele-Shaw type equation involving a degenerate operato…