3 citations · 7 across the 16 of their papers we have counts for
18 papers
Regularity for the normalized p-Laplacian equation with an arbitrary degeneracy law
Claudemir Alcantara, Makson Santos
We examine the interior regularity of solutions to a degenerate normalized -Laplace equation, where the degeneracy is governed by a modulus of continuity whose inverse satisfies…
Comparison Principle, A.B.P.-type estimates for solutions of quasi-linear elliptic equations in non-divergence form and some implications
Junior da S. Bessa, Reshmi Biswas, João Vitor da Silva +2
In this work, we establish global gradient estimates to solutions of quasilinear elliptic models in non-divergence form with general degeneracy law and a Hamiltonian term, given by…
Higher regularity estimates for solutions to -Laplacian-type models
João Vitor da Silva, Makson S. Santos, Mayra Soares
In this work, we tackle the higher regularity estimates of solutions to inhomogeneous Laplacian equations at interior critical points. Our estimates provide smoothness pro…
Global fractional Sobolev regularity for fully nonlinear elliptic equations
Claudemir Alcantara, Makson Santos
We investigate fractional regularity estimates up to the boundary for solutions to fully nonlinear elliptic equations with measurable ingredients. Specifically, under the assumptio…
Optimal Regularity for Fully Nonlinear Nonlocal Equations with Unbounded Source Terms
Disson S. dos Prazeres, Makson S. Santos
We prove optimal regularity estimates for viscosity solutions to a class of fully nonlinear nonlocal equations with unbounded source terms. More precisely, depending on the integra…
Free boundary regularity for a spectral optimal partition problem with volume and inclusion constraints
Dario Mazzoleni, Makson S. Santos, Hugo Tavares
This paper is devoted to a complete characterization of the free boundary of all solutions to the following spectral -partition problem with measure and inclusion constraints: \…
Schauder and Calderón-Zygmund type estimates for fully nonlinear parabolic equations under "small ellipticity aperture" and applications
João Vitor da Silva, Makson S. Santos
In this manuscript, we derive Schauder estimates for viscosity solutions to non-convex fully nonlinear second-order parabolic equations \[ \partial_t u - F(x, t,D^2u) = f (x, t) \q…
Spectral partition problems with volume and inclusion constraints
Pêdra D. S. Andrade, Ederson Moreira dos Santos, Makson S. Santos +1
In this paper, we discuss a class of spectral partition problems with a measure constraint, for partitions of a given bounded connected open set. We establish the existence of an o…
Sharp regularity estimates for a singular inhomogeneous (m, p)-Laplacian equation
Pêdra D. S. Andrade, João Vitor da Silva, Giane C. Rampasso +1
In this paper, we investigate a class of doubly nonlinear evolutions PDEs. We establish sharp regularity for the solutions in Hölder spaces. The proof is based on the geometric tan…
Regularity estimates for fully nonlinear integro-differential equations with nonhomogeneous degeneracy
Pêdra D. S. Andrade, Disson S. dos Prazeres, Makson S. Santos
We investigate the regularity of the solutions for a class of degenerate/singular fully nonlinear nonlocal equations. In the degenerate scenario, we establish that there exists at…
Fractional Sobolev regularity for fully nonlinear elliptic equations
Edgard A. Pimentel, Makson S. Santos, Eduardo V. Teixeira
We prove higher-order fractional Sobolev regularity for fully nonlinear, uniformly elliptic equations in the presence of unbounded source terms. More precisely, we show the existen…
Improved regularity for the parabolic normalized p-Laplace equation
Pêdra D. S. Andrade, Makson S. Santos
We derive regularity estimates for viscosity solutions to the parabolic normalized p-Laplace. By using approximation methods and scaling arguments for the normalized p-parabolic op…
Hölder regularity for non-variational porous media type equations
Héctor A. Chang-Lara, Makson S. Santos
We present a Krylov-Safonov theory approach for the Hölder regularity of viscosity solutions to non-variational porous media type equations. We explore the peculiarity of this type…
A fully nonlinear free transmission problem
Edgard A. Pimentel, Makson S. Santos
We examine a free transmission problem driven by fully nonlinear elliptic operators. Since the transmission interface is determined endogeneously, our analysis is two-fold: we stud…
Improved regularity for the -Poisson equation
Edgard A. Pimentel, Giane C. Rampasso, Makson S. Santos
In this paper we produce new, optimal, regularity results for the solutions to -Poisson equations. We argue through a delicate approximation method, under a smallness regime for…
Geometric regularity theory for a time-dependent Isaacs equation
Pêdra D. S. Andrade, Giane C. Rampasso, Makson S. Santos
The purpose of this work is to produce a regularity theory for a class of parabolic Isaacs equations. Our techniques are based on approximation methods which allow us to connect ou…
Improved regularity for the porous medium equation along zero level-sets
Edgard A Pimentel, Makson S. Santos
In the present work we establish sharp regularity estimates for the solutions of the porous medium equation, along their zero level-sets. We work under a proximity regime on the ex…
Geometric regularity for elliptic equations in double-divergence form
Raimundo Leitão, Edgard A. Pimentel, Makson S. Santos
In this paper, we examine the regularity of the solutions to the double-divergence equation. We establish improved Hölder continuity as solutions approach their zero level-sets. In…