8 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^…
From qualitative smoothness to uniform estimates for fully nonlinear elliptic equations
Aelson Sobral, Eduardo V. Teixeira
We establish a general mechanism that turns qualitative smoothness into uniform, quantitative regularity estimates for fully nonlinear elliptic equations. The central conclusion is…
Endpoint Differentiability Moduli for Fully Nonlinear Elliptic Equations
Aelson Sobral, Eduardo V. Teixeira
A classical consequence of Caffarelli's fully nonlinear regularity theory [L. A. Caffarelli, Ann. of Math. (2) 130 (1989), no. 1, 189-213] is that viscosity solutions of uniformly…
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…
Uniform Lipschitz regularity for two-phase singularly perturbed fully nonlinear elliptic equations
Thialita M. Nascimento, Aelson Sobral, Eduardo V. Teixeira
We study sign-changing viscosity solutions of the singularly perturbed fully nonlinear equation $$ F(D^2u_\varepsilon) = \fracα{\varepsilon} β\left(\frac{u_\varepsilon}{\varepsilon…
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…
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…
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…