arXiv subjects

Antonio Vitolo

Publications and source records attributed to Antonio Vitolo.

7 recordsLinked to original sources

arXiv2019

Regularity properties for a class of non-uniformly elliptic Isaacs operators

We consider the elliptic differential operator defined as the sum of the minimum and the maximum eigenvalue of the Hessian matrix, which can be viewed as a degenerate elliptic Isaacs operator, in dimension larger than two. Despite of nonlinearity, degeneracy, non-concavity and non-convexity, such operator generally enjoys the qualitative properties of the Laplace operator, as for instance maximum and comparison principles, ABP and Harnack inequalities, Liouville theorems for subsolutions or supersolutions. Existence and uniqueness for the Dirichlet problem are also proved as well as local and global Holder estimates for viscosity solutions. All results are discussed for a more general class of weighted partial trace operators.

math.AP↗

arXiv2019

Directional ellipticity on special domains: weak Maximum and Phragmèn-Lindelöf principles

We prove the validity of maximum principles for a class of fully nonlinear operators on unbounded subdomains $Ω\subset \mathbb R^n$ of cylindrical type. The main structural assumption is the uniform ellipticity of the operator along the bounded directions of $Ω$, with possible degeneracy along the unbounded directions.

math.AP↗

arXiv2016

Removable singularities for degenerate elliptic Pucci operators

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, with the aim to extend maximum principles and removable singularities results to cases of highly degenerate ellipticity.nn

math.AP↗

arXiv2015

Entire solutions of fully nonlinear elliptic equations with a superlinear gradient term

In this paper we consider second order fully nonlinear operators with an additive superlinear gradient term. Like in the pioneering paper of Brezis for the semilinear case, we obtain the existence of entire viscosity solutions, defined in all the space, without assuming global bounds. A uniqueness result is also obtained for special gradient terms, subject to a convexity/concavity type assumption where superlinearity is essential and has to be handled in a different way from the linear case.

math.AP↗

arXiv2015

Entire subsolutions of fully nonlinear degenerate elliptic equations

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 entire sub solutions.

math.AP↗

arXiv2015

On the inequality $F(x,D^2u) \geq f(u)+g(u)|Du|^q$

We consider fully nonlinear degenerate elliptic equations with zero and first order terms. We provide a priori upper bounds and characterize the existence of entire subsolutions under growth conditions on the lower order coefficients which extend the classical Keller--Osserman condition for semilinear equations.

math.AP↗

arXiv2014

ABP and global Holder estimates for fully nonlinear elliptic equations in unbounded domains

We prove global Holder estimates for solution of fully nonlinear elliptic or degenerate elliptic equations in unbounded domains under geometric conditions on the domain a' la Cabre'.

math.AP↗