10 papers · 1 filter
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…
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…
Optimal regularity for degenerate elliptic equations with Hamiltonian terms
Pêdra D. S. Andrade, Thialita M. Nascimento
We establish optimal, quantitative Höder estimates for the gradient of solutions to a class of degenerate elliptic equations with Hamiltonian terms. The presence of such lower-orde…
Regularity of solutions to degenerate and singular free boundary problems with volume constraint
T. M. Nascimento, X. H. Nguyen, P. R. Stinga
We prove existence and regularity of solutions to degenerate and singular elliptic free boundary problems, where the volume of the positivity set of the solution is prescribed.
Interior regularity estimates for fully nonlinear equations with arbitrary nonhomogeneous degeneracy laws
Pêdra D. S. Andrade, Thialita M. Nascimento
In this paper, we study regularity estimates for a class of degenerate, fully nonlinear elliptic equations with arbitrary nonhomogeneous degeneracy laws. We establish that viscosit…
Improved regularity estimates for Hardy-Hénon-type equations driven by the -Laplacian
Elzon C. Bezerra Júnior, João Vitor da Silva, Thialita M. Nascimento +1
In this work, we establish sharp and improved regularity estimates for viscosity solutions of Hardy-Hénon-type equations with possibly singular weights and strong absorption govern…
Schauder-type estimates for fully nonlinear degenerate elliptic equations
Thialita M. Nascimento
In this paper, we examine regularity estimates for solutions to fully nonlinear, degenerated elliptic equations, at interior vanishing source points. At these points, we obtain Sch…
Higher regularity of solutions to fully nonlinear elliptic equations
Thialita M. Nascimento, Ginaldo Sá, Aelson Sobral +1
We establish higher regularity properties of solutions to fully nonlinear elliptic equations at interior critical points. The key novelty of our estimates lies in the fact that the…
New regularity estimates for fully nonlinear elliptic equations
Thialita M. Nascimento, Eduardo V. Teixeira
We establish new quantitative Hessian integrability estimates for viscosity supersolutions of fully nonlinear elliptic operators. As a corollary, we show that the optimal Hessian p…