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I. Birindelli

Publications and source records attributed to I. Birindelli.

14 recordsLinked to original sources
arXiv2020

Existence issues for a large class of degenerate elliptic equations with nonlinear Hamiltonians

We give sufficient conditions for the existence and uniqueness, in bounded uniformly convex domains $Ω$, of solutions of degenerate elliptic equations depending also on the nonlinear gradient term $H$, in term of the size of $Ω$, of the forcing term $f$ and of $H$. The results apply to a wide class of equations, having as principal part significant examples, e.g. linear degenerate operators, weighted partial trace operators and the homogeneous Monge-Ampère operator.

math.AP↗
arXiv2012

${\cal C}^{1,β}$ regularity for Dirichlet problems associated to fully nonlinear degenerate elliptic equations

In this paper we prove Holder regularity of the gradient for solutions of Dirichlet problem associate to degenerate elliptic equations, extending the recent result of Imbert and Silvestre. Indeed we obtain regularity up to the boundary and when the equation has lower order terms.The proof follows their scheme but requires new tools and new ideas. In particular we give some a priori Lipschitz and Hölder estimates in the presence of boundary condition on one part of the boundary.

math.AP↗
arXiv2011

Overdetermined problems for fully non linear operators

In this paper, we consider the overdetermined problem for fully non linear singular or degenerate elliptic operators in bounded smooth domains with both Dirichlet and Neumann condition, as in the classical result of Serrin we prove that the existence of nontrivial constant sign solution imply that the domain is a ball.

math.AP↗
arXiv2010

A Neumann eigenvalue problem for fully nonlinear operators

In this paper we study the asymptotic behavior of the principal eigenvalues associated to the Pucci operator in bounded domain $Ω$ with Neumann/Robin boundary condition i.e. $\partial_n u=αu$ when $α$ tends to infinity. This study requires Lipschitz estimates up to the boundary that are interesting in their own rights.

math.AP↗
arXiv2010

One-dimensional symmetry for solutions of Allen Cahn fully nonlinear equations

This article presents some qualitative results for entire solutions of the fully nonlinear elliptic equations of Allen Cahn type . Precisely under some additional assumptions on the forcing term, if the solution is bounded and converges uniformly at infinity in a fixed direction to its extrema, then the solution depends only on one variable.

math.AP↗
arXiv2008

Eigenvalue and Dirichlet problem for fully-nonlinear operators in non smooth domains

In this paper we study the maximum principle, the existence of eigenvalue and the existence of solution for the Dirichlet problem for operators which are fully-nonlinear, elliptic but presenting some singularity or degeneracy which are similar to those of the p-Laplacian, the novelty resides in the fact that we consider the equations in bounded domains which only satisfy the exterior cone condition.

math.AP↗
arXiv2006

The Dirichlet problem for singular fully nonlinear operators

In this paper we prove existence of (viscosity) solutions of Dirichlet problems concerning fully nonlinear elliptic operator, which are either degenerate or singular when the gradient of the solution is zero. For this class of operators it is possible to extend the concept of eigenvalue, this paper concerns the cases when the inf of the principal eigenvalues is positive i.e. when both the maximum and the minimum principle holds.

math.AP↗
arXiv2006

Eigenvalue, maximum principle and regularity for fully non linear homogeneous operators

The main scope of this article is to define the concept of principal eigenvalue for fully non linear second order operators in bounded domains that are elliptic and homogenous. In particular we prove maximum and comparison principle, Holder and Lipschitz regularity. This leads to the existence of a first eigenvalue and eigenfunction and to the existence of solutions of Dirichlet problems within this class of operators.

math.AP↗
arXiv2006

The Ginzburg-Landau equation in the Heisenberg group

We consider a functional related with phase transition models in the Heisenberg group framework. We prove that level sets of local minimizers satisfy some density estimates, that is, they behave as "codimension one" sets. We thus deduce a uniform convergence property of these level sets to interfaces with minimal area. These results are then applied in the construction of (quasi)periodic, plane-like minimizers, i.e., minimizers of our functional whose level sets are contained in a spacial slab of universal size in a prescribed direction. As a limiting case, we obtain the existence of hypersurfaces contained in such a slab which minimize the surface area with respect to a given periodic metric.

math.AP↗
arXiv2001

Some Liouville Theorems for the p-Laplacian

We present several Liouville type results for the $p$-Laplacian in $\R^N$. Suppose that $h$ is a nonnegative regular function such that $$ h(x) = a|x|^γ {\rm for}\ |x|\ {\rm large},\ a>0\ {\rm and}\ γ> -p. $$ We obtain the following non -existence result: 1) Suppose that $N>p>1$, and $u\in W^{1,p}_{loc} (\R^N)\cap {\cal C} (\R^N)$ is a nonnegative weak solution of $ - {\rm div} (|\nabla u|^{p-2 }\nabla u) \geq h(x) u^q \;\;\mbox{in }\; \R^N $ . Suppose that $p-1< q\leq {(N+γ)(p-1)\over N-p}$ then $u\equiv 0$. 2) Let $N\leq p$. If $u\in W^{1,p}_{loc} (\R^N)\cap {\cal C} (\R^N)$ is a weak solution bounded below of $-{\rm div} (|\nabla u|^{p-2 }\nabla u)\geq 0$ in $\R^N$ then $u$ is constant. 3) Let $N>p$ if $u$ is bounded from below and $-{\rm div} (|\nabla u|^{p-2 }\nabla u)=0$ in $\R^N$ then $u$ is constant. 4)If $ -Δ_p u+h(x) u^q\leq 0, $. If $q> p-1$, then $u\equiv 0$.

math.AP↗