In this paper, we review some results over the last 10-15 years on elliptic and parabolic
equations with discontinuous coefficients. We begin with an approach given by NV Krylov to …

This paper studies a priori and regularity estimates of Evans-Krylov type in Hölder spaces for
fully nonlinear uniformly elliptic and parabolic equations of second order when the operator …

We establish sharp C_ loc^ 1, β C loc 1, β geometric regularity estimates for bounded
solutions of a class of fully nonlinear elliptic equations with non-homogeneous degeneracy …

In the present paper, we propose the investigation of variable-exponent,
degenerate/singular elliptic equations in non-divergence form. This current endeavor …

We study an equation governed by a discontinuous fully nonlinear operator. Such
discontinuities are solution-dependent, which introduces a free boundary. Working under …

We study a free transmission problem driven by degenerate fully nonlinear operators. Our
first result concerns the existence of a viscosity solution to the associated Dirichlet problem …

The obstacle problem for a class of degenerate fully nonlinear operators Page 1 Rev. Mat.
Iberoam. 37 (2021), no. 5, 1991–2020 doi 10.4171/rmi/1256 c 2021Real Sociedad …

Presenting the basics of elliptic PDEs in connection with regularity theory, the book bridges
fundamental breakthroughs-such as the Krylov-Safonov and Evans-Krylov results …

We develop an optimal regularity theory for L p-viscosity solutions of fully nonlinear
uniformly elliptic equations in nondivergence form whose gradient growth is described …

We consider fully nonlinear uniformly elliptic equations with quadratic growth in the gradient,
such as− F (x, u, D u, D 2 u)= λ c (x) u+< M (x) D u, D u>+ h (x) in a bounded domain with a …