28 citations · 74 across the 22 of their papers we have counts for
26 papers
Fully Nonlinear Logistic Equations with Sanctuary Regions and Nonlocal Diffusion
Giulio Galise, Shuhei Kitano
We study positive solutions of in a bounded domain, where , the nonnegative coefficient may vanish on a sanctuary region, and is a fully nonlinear nonl…
Balance between degenerate elliptic operators and coercive Hamiltonians
Isabeau Birindelli, Giulio Galise, Hitoshi Ishii
For , we consider the boundary value problem for fully nonlinear degenerate elliptic equations in bounded domains with Dirichlet or boundary blow-u…
Fully nonlinear logistic equations with sanctuary
Isabeau Birindelli, Giulio Galise, Fabiana Leoni
For the fully nonlinear stationary logistic equation with and , in a bounded domain with Dirichlet boundary condition, we determ…
Liouville type results for the fractional truncated Laplacians in a half-space
Giulio Galise, Hitoshi Ishii
Existence issues of viscosity supersolutions in the half-space , for a class of fully nonlinear integral equations involving the fractional truncated Laplacians and…
Liouville results for semilinear integral equations with conical diffusion
Isabeau Birindelli, Lele Du, Giulio Galise
Nonexistence results for positive supersolutions of the equation are obtained, being any symmetric and stable linear operator, positi…
Nonlocal degenerate Isaacs operators: Hölder regularity
Isabeau Birindelli, Giulio Galise, Yannick Sire
We show that bounded viscosity solutions of some nonlocal degenerate Isaacs type operators of order are Hölder continuous, provided is sufficiently close to 1. As an appli…
Propagation of minima for nonlocal operators
Isabeau Birindelli, Giulio Galise, Hitoshi Ishii
In this paper we state some sharp maximum principle, i.e. we characterize the geometry of the sets of minima for supersolutions of equations involving the -\emph{th fractional t…
Maximum principles and related problems for a class of nonlocal extremal operators
Isabeau Birindelli, Giulio Galise, Delia Schiera
We study the validity of the comparison and maximum principles, and their relation with principal eigenvalues, for a class of degenerate nonlinear operators that are extremal among…
A regularity result for a class of non-uniformly elliptic operators
Fausto Ferrari, Giulio Galise
We obtain an explicit Hölder regularity result for viscosity solutions of a class of second order fully nonlinear equations leaded by operator that are neither convex/concave nor u…
Fractional truncated Laplacians: representation formula, fundamental solutions and applications
Isabeau Birindelli, Giulio Galise, Erwin Topp
In this note we introduce some nonlinear extremal nonlocal operators that approximate the, so called, truncated Laplacians. For these operators we construct representation formulas…
Existence issues for a large class of degenerate elliptic equations with nonlinear Hamiltonians
I. Birindelli, G. Galise, A. Rodríguez
We give sufficient conditions for the existence and uniqueness, in bounded uniformly convex domains , of solutions of degenerate elliptic equations depending also on the nonline…
Allen-Cahn equation for the truncated Laplacian: unusual phenomena
Isabeau Birindelli, Giulio Galise
We study entire viscosity solutions of the Allen-Cahn type equation for the truncated Laplacian that are either one dimensional or radial, in order to shed some light on a possible…
New concentration phenomena for a class of radial fully nonlinear equations
Giulio Galise, Alessandro Iacopetti, Fabiana Leoni +1
We study radial sign-changing solutions of a class of fully nonlinear elliptic Dirichlet problems in a ball, driven by the extremal Pucci's operators and with a power nonlinear ter…
Positivity sets of supersolutions of degenerate elliptic equations and the strong maximum principle
Isabeau Birindelli, Giulio Galise, Hitoshi Ishii
We investigate positivity sets of nonnegative supersolutions of the fully nonlinear elliptic equations in , where is an open subset of , an…
Liouville-type results in exterior domains for radial solutions of fully nonlinear equations
Giulio Galise, Alessandro Iacopetti, Fabiana Leoni
We give necessary and sufficient conditions for the existence of positive radial solutions for a class of fully nonlinear uniformly elliptic equations posed in the complement of a…
The Dirichlet problem for fully nonlinear degenerate elliptic equations with a singular nonlinearity
Isabeau Birindelli, Giulio Galise
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 esta…
Existence through convexity for the truncated Laplacians
Isabeau Birindelli, Giulio Galise, Hitoshi Ishii
We study the Dirichlet problem on a bounded convex domain of , with zero boundary data, for truncated Laplacians , with . We establish a neces…
Towards a reversed Faber-Krahn inequality for the truncated Laplacian
Isabeau Birindelli, Giulio Galise, Hitoshi Ishii
We consider the nonlinear eigenvalue problem, with Dirichlet boundary condition, for a class of very degenerate elliptic operators, with the aim to show that, at least for square t…
Concentration and energy invariance for a class of fully nonlinear elliptic equations
Isabeau Birindelli, Giulio Galise, Fabiana Leoni +1
We study the asymptotic behaviour of positive solutions of fully nonlinear elliptic equations in a ball, as the exponent of the power nonlinearity approaches a critical value. We s…
On positive solutions of fully nonlinear degenerate Lane-Emden type equations
Giulio Galise
We prove existence and uniqueness results of positive viscosity solutions of fully nonlinear degenerate elliptic equations with power-like zero order perturbations in bounded domai…
Liouville theorems for a family of very degenerate elliptic non linear operators
Isabeau Birindelli, Giulio Galise, Fabiana Leoni
We prove nonexistence results of Liouville type for nonnegative viscosity solutions of some equations involving the fully nonlinear degenerate elliptic operators ,…
A family of degenerate elliptic operators: maximum principle and its consequences
Isabeau Birindelli, Giulio Galise, Hitoshi Ishii
In this paper we investigate the validity and the consequences of the maximum principle for degenerate elliptic operators whose higher order term is the sum of "k" eigenvalues of t…
Removable singularities for degenerate elliptic Pucci operators
Giulio Galise, Antonio Vitolo
In this paper we introduce some fully nonlinear second order operators defined as weighted partial sums of the eigenvalues of the Hessian matrix, arising in geometrical contexts, w…
Existence results for fully nonlinear equations in radial domains
Giulio Galise, Fabiana Leoni, Filomena Pacella
We consider the fully nonlinear problem \begin{equation*} \begin{cases} -F(x,D^2u)=|u|^{p-1}u & \text{in }\\ u=0 & \text{on } \end{cases} \end{equation*} where is…