Related papers: Fully nonlinear free transmission problems with no…
We study degenerate fully nonlinear free transmission problems, where the degeneracy rate varies in the domain. We prove optimal pointwise regularity depending on the degeneracy rate. Our arguments consist of perturbation methods, relating…
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 framing the equation in the context of viscosity inequalities,…
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 study the regularity of the solutions and some geometric…
We study a fully nonlinear free transmission problem in the presence of general degeneracy laws. Under minimal conditions on the degeneracy of the model, we establish the differentiability of viscosity solutions.
We propose finite difference methods for degenerate fully nonlinear elliptic equations and prove the convergence of the schemes. Our focus is on the pure equation and a related free boundary problem of transmission type. The cornerstone of…
We study transmission problems with free interfaces from one random medium to another. Solutions are required to solve distinct partial differential equations, $\mbox{L}_{+}$ and $\mbox{L}_{-}$, within their positive and negative sets…
In this manuscript we prove the existence of solutions to a fully nonlinear system of (degenerate) elliptic equations of Lane-Emden type and discuss a inhomogeneous generalization.
We study an equation governed by a discontinuous fully nonlinear operator. Such discontinuities are solution-dependent, which introduces a free boundary. Working under natural assumptions, we prove the existence of $L^p$-viscosity and…
In this manuscript we study geometric regularity estimates for problems driven by fully nonlinear elliptic operators under strong absorption conditions. We establish improved geometric regularity along the free boundary, for a sharp value…
We examine boundary regularity for a fully nonlinear free transmission problem. We argue using approximation methods, comparing the operators driving the problem with a limiting profile. Working natural conditions on the data of the…
In this paper, we present a problem involving fully nonlinear elliptic operators with Hamiltonian, which can present a singularity or degenerate as the gradient approaches the origin. The model studied here, allows the appearance of plateau…
We prove estimates and existence results for some fully nonlinear elliptic equations on Riemannian manifolds. These equations are not arbitrary, but arise naturally in the study of conformal geometry.
We develop the regularity theory of viscosity solutions to transmission problems for fully nonlinear second order uniformly elliptic equations. Our results give a complete theory of existence, uniqueness, comparison principle, and…
We establish sharp geometric Holder regularity estimates for Gradient for bounded solutions of a class of fully nonlinear elliptic equations with non-homogeneous degeneracy. Such regularity estimates simplify and generalize, to some extent,…
The goal of this paper is to study some possibly degenerate elliptic equation in a bounded domain with a nonlinear boundary condition involving measure data. We investigate two types of problems: the first one deals with the laplacian in a…
We study non-variational degenerate elliptic equations with high order singular structures. No boundary data are imposed and singularities occur along an {\it a priori} unknown interior region. We prove that positive solutions have a…
We study a free transmission problem in which solution minimizes a functional with different definitions in positive and negative phase of function. We prove some asymptotic regularity results when the jumps of the diffusion coefficients…
As an application of the theory of linear parabolic differential equations on noncompact Riemannian manifolds, developed in earlier papers, we prove a maximal regularity theorem for nonuniformly parabolic boundary value problems in…
We prove existence and non existence results for fully nonlinear degenerate elliptic inequalities, by showing that the classical Keller--Osserman condition on the zero order term is a necessary and sufficient condition for the existence of…
We prove new borderline regularity results for solutions to fully nonlinear elliptic equations together with pointwise gradient potential estimates.