12 papers
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…
Sharp Hessian integrability for fully nonlinear elliptic supersolutions in low dimensions
Thialita M. Nascimento, Eduardo V. Teixeira
We settle the planar sharp Hessian-integrability conjecture of Armstrong, Silvestre, and Smart [\emph{Comm. Pure Appl. Math.} \textbf{65} (2012), 1169--1184] for viscosity supersol…
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…
Borderline regularity in singular free boundary problems
Damião J. Araújo, Aelson Sobral, Eduardo V. Teixeira +1
In this paper, we investigate the borderline regularity of local minimizers of energy functionals under minimal assumptions on the potential term . When is merely bounded an…