20 citations · 31 across the 20 of their papers we have counts for
30 papers
Transmission problems: regularity theory, interfaces and beyond
Vincenzo Bianca, Edgard A. Pimentel, José Miguel Urbano
Modelling diffusion processes in heterogeneous media requires addressing inherent discontinuities across interfaces, where specific conditions are to be met. These challenges fall…
Improved regularity for a Hessian-dependent functional
Vincenzo Bianca, Edgard A. Pimentel, José Miguel Urbano
We prove that minimizers of the -norm of the Hessian in the unit ball of are locally of class . Our findings extend previous results on Hessian-depen…
BMO-regularity for a degenerate transmission problem
Vincenzo Bianca, Edgard A. Pimentel, José Miguel Urbano
We examine a transmission problem driven by a degenerate quasilinear operator with a natural interface condition. Two aspects of the problem entail genuine difficulties in the anal…
Flipping regularity via the Harnack approach and applications to nonlinear elliptic problems
Diego R. Moreira, Edgard A. Pimentel
We prove an abstract result ensuring that one-sided geometric control yields two-sided estimates for functions satisfying general conditions. Our findings resonate in the context o…
Fully nonlinear Hamilton-Jacobi equations of degenerate type
David Jesus, Edgard A. Pimentel, José Miguel Urbano
We examine Hamilton-Jacobi equations driven by fully nonlinear degenerate elliptic operators in the presence of superlinear Hamiltonians. By exploring the Ishii-Jensen inequality,…
Potential estimates for fully nonlinear elliptic equations with bounded ingredients
Edgard A. Pimentel, Miguel Walker
We examine -viscosity solutions to fully nonlinear elliptic equations with bounded-measurable ingredients. By considering , we focus on gradient-regularity estimates…
-regularity for degenerate diffusion equations
Pêdra Andrade, Daniel Pellegrino, Edgard A. Pimentel +1
We prove that any solution of a degenerate elliptic PDE is of class , provided the inverse of the equation's degeneracy law satisfies an integrability criterium, viz. $σ^{-1}…
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…
A Hessian-dependent functional with free boundaries and applications to mean-field games
Julio C. Correa, Edgard A. Pimentel
We study a Hessian-dependent functional driven by a fully nonlinear operator. The associated Euler-Lagrange equation is a fully nonlinear mean-field game with free boundaries. Our…
Existence of solutions to a fully nonlinear free transmission problem
Edgard A. Pimentel, Andrzej Święch
We study an equation governed by a discontinuous fully nonlinear operator. Such discontinuities are solution-dependent, which introduces a free boundary. Working under natural assu…
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…
Stationary fully nonlinear mean-field games
Pêdra D. S. Andrade, Edgard A. Pimentel
In this paper we examine fully nonlinear mean-field games associated with a minimization problem. The variational setting is driven by a functional depending on its argument throug…
A note on the density of the partial regularity result in the class of viscosity solutions
Disson dos Prazeres, Edgard A. Pimentel, Giane C. Rampasso
We establish the density of the partial regularity result in the class of continuous viscosity solutions. Given a fully nonlinear equation, we prove the existence of a sequence ent…
Non-convex Hamilton-Jacobi equations with gradient constraints
Héctor A. Chang-Lara, Edgard A. Pimentel
We study non-convex Hamilton-Jacobi equations in the presence of gradient constraints and produce new, optimal, regularity results for the solutions. A distinctive feature of those…
A fully nonlinear degenerate free transmission problem
Gerardo Huaroto, Edgard A. Pimentel, Giane C. Rampasso +1
We study a free transmission problem driven by degenerate fully nonlinear operators. Our first result concerns the existence of solutions to the associated Dirichlet problem. By fr…
Existence and improved regularity for a nonlinear system with collapsing ellipticity
Edgard A. Pimentel, José Miguel Urbano
We study a nonlinear system made up of an elliptic equation of blended singular/degenerate type and Poisson's equation with a lowly integrable source. We prove the existence of a w…
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…
On a Mean Field Optimal Control Problem
Jose A. Carrillo, Edgard A. Pimentel, Vardan K. Voskanyan
In this paper we consider a mean field optimal control problem with an aggregation-diffusion constraint, where agents interact through a potential, in the presence of a Gaussian no…
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…
Regularity of solutions to a class of variable-exponent fully nonlinear elliptic equations
Anne C. Bronzi, Edgard A. Pimentel, Giane C. Rampasso +1
In the present paper, we propose the investigation of variable-exponent, degenerate/singular elliptic equations in non-divergence form. This current endeavor parallels the by now w…
Regularity theory for the Isaacs equation through approximation methods
Edgard A. Pimentel
In this paper, we propose an approximation method to study the regularity of solutions to the Isaacs equation. This class of problems plays a paramount role in the regularity theor…
Interior Sobolev regularity for fully nonlinear parabolic equations
Ricardo Castillo, Edgard A. Pimentel
In the present paper, we establish sharp Sobolev estimates for solutions of fully nonlinear parabolic equations, under minimal, asymptotic, assumptions on the governing operator. I…
Singular mean-filed games
Marco Cirant, Diogo A. Gomes, Edgard A. Pimentel +1
Here, we prove the existence of smooth solutions for mean-field games with a singular mean-field coupling; that is, a coupling in the Hamilton-Jacobi equation of the form $g(m)=-m^…