47 citations · 84 across the 9 of their papers we have counts for
11 papers
Sharp regularity for singular obstacle problems
Damião J. Araújo, Rafayel Teymurazyan, Vardan Voskanyan
We obtain sharp local regularity of solutions for singular obstacle problems, Euler-Lagrange equation of which is given by …
An optimal Liouville theorem for the porous medium equation
Damião J. Araújo, Rafayel Teymurazyan
Under a sharp asymptotic growth condition at infinity, we prove a Liouville type theorem for the inhomogeneous porous medium equation, provided it stays universally close to the he…
Sharp boundary and global regularity for degenerate fully nonlinear elliptic equations
Damião Araújo, Boyan Sirakov
We obtain optimal boundary and global regularity estimates for viscosity solutions of fully nonlinear elliptic equations whose ellipticity degenerates at the critical points of a g…
Infinity Laplacian equations with singular absorptions
Damião J. Araújo, Ginaldo de Santana Sá
In this work, we study regularity properties for nonvariational singular elliptic equations ruled by the infinity Laplacian. We obtain optimal regularity along the free b…
Fully nonlinear dead-core systems
Damião J. Araújo, Rafayel Teymurazyan
We study fully nonlinear dead-core systems coupled with strong absorption terms. We discover a chain reaction, exploiting properties of an equation along the system and obtain high…
Detecting the completeness of a Finsler manifold via potential theory for its infinity Laplacian
Damião J. Araújo, Luciano Mari, Leandro F. Pessoa
In this paper, we study some potential theoretic aspects of the eikonal and infinity Laplace operator on a Finsler manifold . Our main result shows that the forward completeness…
Higher regularity estimates for the porous medium equation near the Heat equation
Damião J. Araújo
In this paper we investigate regularity aspects for solutions of the nonlinear parabolic equation usually called the porous medium equation. More preci…
A proof of the -regularity conjecture in the plane
Damião J. Araújo, Eduardo V. Teixeira, José Miguel Urbano
We establish a new oscillation estimate for solutions of nonlinear partial differential equations of elliptic, degenerate type. This new tool yields a precise control on the growth…
On a two-phase free boundary problem ruled by the infinity Laplacian
Damião J. Araújo, Eduardo Teixeira, José Miguel Urbano
In this paper we consider a two-phase free boundary problem ruled by the infinity Laplacian. Our main result states that bounded viscosity solutions in are universally Lipsch…
Infinity Laplacian equation with strong absorptions
Damião J. Araújo, Raimundo Leitão, Eduardo V. Teixeira
We study regularity properties of solutions to reaction-diffusion equations ruled by the infinity laplacian operator. We focus our analysis in models presenting plateaus, i.e. regi…
Optimal gradient continuity for degenerate elliptic equations
Damião J. Araújo, Gleydson C. Ricarte, Eduardo V. Teixeira
We establish new, optimal gradient continuity estimates for solutions to a class of 2nd order partial differential equations, , whose diffusion…