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math.AP2026
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…
math.AP2026
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…
math.AP2026
Geometric Estimates for Solutions of Semilinear Equations with Singular Potentials
Thialita M. Nascimento, Lei Zhang
In this work, we study local minimizers of elliptic functionals with strong absorption terms and unbounded, sign-changing sources. These problems naturally interpolate between two…