Related papers: Fully nonlinear free transmission problems with no…
We derive the solvability and regularity of the Dirichlet problem for fully non-linear elliptic equations possibly with degenerate right-hand side on Hermitian manifolds, through establishing a quantitative version of boundary estimate…
We consider fully nonlinear obstacle-type problems of the form \begin{equation*} \begin{cases} F(D^{2}u,x)=f(x) & \text{a.e. in}B_{1}\cap\Omega,|D^{2}u|\le K & \text{a.e. in}B_{1}\backslash\Omega, \end{cases} \end{equation*} where $\Omega$…
We establish Liouville type theorems for degenerate conformally invariant equations.
We formulate and study an elliptic transmission-like problem combining local and nonlocal elements. Let $\mathbb{R}^{n}$ be separated into two components by a smooth hypersurface $\Gamma$. On one side of $\Gamma$, a function satisfies a…
We examine Hamilton-Jacobi equations driven by fully nonlinear degenerate elliptic operators in the presence of superlinear Hamiltonians. By exploring the Ishii-Jensen inequality, we prove that viscosity solutions are locally…
We prove sharp regularity estimates for solutions of highly degenerate fully nonlinear elliptic equations. These are free boundary models in which a nonlinear diffusion process drives the system only in the region where the gradient…
We prove that bounded solutions to an overdetermined fully nonlinear free boundary problem in the plane are one dimensional. Our proof relies on maximum principle techniques and convexity arguments.
We derive a priori second order estimates for solutions of a class of fully nonlinear elliptic equations on Riemannian manifolds under some very general structure conditions. We treat both equations on closed manifolds, and the Dirichlet…
We give a simplified presentation of the obstacle problem approach to stochastic homogenization for elliptic equations in nondivergence form. Our argument also applies to equations which depend on the gradient of the unknown function. In…
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…
In this paper we study the fully nonlinear free boundary problem $$ {{array}{ll} F(D^2u)=1 & \text{a.e. in}B_1 \cap \Omega |D^2 u| \leq K & \text{a.e. in}B_1\setminus\Omega, {array}. $$ where $K>0$, and $\Omega$ is an unknown open set. Our…
This paper deals with regularity theory for two-phase free boundary variational problems ruled by degenerate elliptic operators.
We establish a positivity property for a class of semilinear elliptic problems involving indefinite sublinear nonlinearities. Namely, we show that any nontrivial nonnegative solution is positive for a class of problems the strong maximum…
We consider an one-phase free boundary problem for a degenerate fully non-linear elliptic operators with non-zero right hand side. We use the approach present in \cite{DeSilva} to prove that flat free boundaries and Lipschitz free…
In this paper, we are concerned with the uniqueness and the non-degeneracy of positive radial solutions for a class of semilinear elliptic equations. Using detailed ODE analysis, we extend previous results to cases where nonlinear terms may…
We give sufficient conditions for the existence and uniqueness, in bounded uniformly convex domains $\Omega$, of solutions of degenerate elliptic equations depending also on the nonlinear gradient term $H$, in term of the size of $\Omega$,…
In this article we prove some Lipschitz estimates and existence result for a class of degenerate fully nonlinear elliptic equations which are a generalization of the pseudo p-Laplacian. The operators are degenerate elliptic at any point…
This article studies the Dirichlet problem for a class of degenerate fully nonlinear elliptic equations on Riemannian manifolds with \textit{mean concave} boundary in the sense that the mean curvature of the boundary is…
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 well established theory of functionals satisfying nonstandard…
We study a nonlinear equation with an elliptic operator having degenerate coercivity. We prove the existence of a W^{1,1}_0 solution which is distributional or entropic, according to the growth assumptions on a lower order term in…