collaborators

7 papers

math.AP2026

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…

math.AP2026

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 solut…

math.AP2026

Fractional -caloric functions are Lipschitz

David Jesus, Aelson Sobral, José Miguel Urbano

We study the parabolic fractional Laplace equation in the degenerate range . We show that weak solutions are Lipschitz continuous…

math.AP2026

On a Weiss-type Almost Monotonicity Formula

Aelson Sobral

We establish a Weiss-type almost-monotonicity formula for a broad class of variable-coefficient energy functionals, assuming only minimal regularity of the coefficients. As an appl…

math.AP2025

On free boundary problems shaped by varying singularities

Damião Araújo, Aelson Sobral, Eduardo V. Teixeira +1

We start the investigation of free boundary variational models featuring varying singularities. The theory depends strongly on the nature of the singular power and how it c…

math.AP2025

Keller-Osserman and Harnack type results for nonlinear elliptic PDE with unbounded ingredients

Boyan Sirakov, Aelson Sobral

We show that the classical Keller-Osserman theorem on the solvability of the equation is valid when is a general operator in divergence form w…