Related papers: Interior regularity estimates for fully nonlinear …

We study a series of regularity results for solutions to a degenerate or singular fully nonlinear integro-differential equation of the form $$- \big( \sigma_{1}(|Du|) + a(x) \sigma_{2}(|Du|) \big) \mathcal{I}_{\tau}(u,x) = f(x).$$ In the…

We consider nonlinear, uniformly elliptic equations with random, highly oscillating coefficients satisfying a finite range of dependence. We prove that homogenization and linearization commute in the sense that the linearized equation…

We prove sharp regularity estimates for viscosity solutions of fully nonlinear parabolic equations of the form \begin{equation}\label{Meq}\tag{Eq} u_t- F(D^2u, Du, X, t) = f(X,t) \quad \mbox{in} \quad Q_1, \end{equation} where $F$ is…

We prove regularity and stochastic homogenization results for certain degenerate elliptic equations in nondivergence form. The equation is required to be strictly elliptic, but the ellipticity may oscillate on the microscopic scale and is…

We establish interior Lipschitz regularity for continuous viscosity solutions of fully nonlinear, conformally invariant, degenerate elliptic equations. As a by-product of our method, we also prove a weak form of the strong comparison…

In this paper, we establish the boundary regularity results for viscosity solutions of fully nonlinear degenerate/singular parabolic equations of the form $$u_t - x_n^{\gamma} F(D^2 u,x,t) = f,$$ where $\gamma<1$. These equations are…

This article concerns optimal estimates for non-homogeneous degenerate elliptic equation with source functions in borderline spaces of integrability. We deliver sharp H\"older continuity estimates for solutions to $p$-degenerate elliptic…

In this work we establish local $C^{2,\alpha}$ regularity estimates for flat solutions to non-convex fully nonlinear elliptic equations provided the coefficients and the source function are of class $C^{0,\alpha}$. For problems with merely…

We investigate the homogeneous Dirichlet problem in uniformly convex domains for a large class of degenerate elliptic equations with singular zero order term. In particular we establish sharp existence and uniqueness results of positive…

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 entitled to the partial regularity result, approximating its…

In this paper, we study fully non-linear elliptic equations in non-divergence form which can be degenerate when "the gradient is small". Typical examples are either equations involving the $m$-Laplace operator or Bellman-Isaacs equations…

We obtain new oscillation and gradient bounds for the viscosity solutions of fully nonlinear degenerate elliptic equations where the Hamiltonian is a sum of a sublinear and a superlinear part in the sense of Barles and Souganidis (2001). We…

We study the higher H\"older regularity of local weak solutions to a class of nonlinear nonlocal elliptic equations with kernels that satisfy a mild continuity assumption. An interesting feature of our main result is that the obtained…

We obtain an explicit H\"older regularity result for viscosity solutions of a class of second order fully nonlinear equations leaded by operator that are neither convex/concave nor uniformly elliptic.

This paper is devoted to the study of uniform $W^{1,\frac{np}{n-p}}$- and $W^{2,p}$-estimates for viscosity solutions to fully nonlinear, uniformly elliptic, periodic homogenization problems, up to boundaries, subject to Dirichlet boundary…

In this paper, we study the regularity of solutions to uniformly degenerate elliptic equations in bounded domains under the condition that the characteristic polynomials have varying characteristic exponents.

We investigate fractional regularity estimates up to the boundary for solutions to fully nonlinear elliptic equations with measurable ingredients. Specifically, under the assumption of uniform ellipticity of the operator, we demonstrate…

We establish regularity results for viscosity solutions to a class of quasilinear parabolic equations exhibiting nonhomogeneous degeneracy or singularity (a double phase regime) of the form \[ u_t - \big(|Du|^{\mathfrak{p}} +…

In this paper, we establish refined regularity estimates for nonnegative solutions to the fractional Poisson equation $$ (-\Delta)^s u(x) =f(x),\,\, x\in B_1(0). $$ Specifically, we have derived H\"{o}lder, Schauder, and Ln-Lipschitz…

We consider viscosity solutions of a class of nonlinear degenerate elliptic equations on bounded domains. We prove comparison principles and a priori supremum bounds for the solutions. We also address the eigenvalue problem and, in many…