146 citations · 289 across the 27 of their papers we have counts for
32 papers
The limit as of the fractional convex envelope
Begoña Barrios, Leandro M. Del Pezzo, Alexander Quaas +1
We study the behavior of the fractional convexity when the fractional parameter goes to 1. For any notion of convexity, the convex envelope of a datum prescribed on the boundary of…
The fundamental solution of the fractional p-laplacian
Leandro M. Del Pezzo, Alexander Quaas
In this article, we find the fundamental solution of the fractional p-laplacian and use them to prove two different Liouville-type theorems. A non-existence classical Liouville-typ…
The evolution problem associated with the fractional first eigenvalue
Begoña Barrios, Leandro M. Del Pezzo, Alexander Quaas +1
In this paper we study the evolution problem associated with the first fractional eigenvalue. We prove that the Dirichlet problem with homogeneous boundary condition is well posed…
Non-simultaneous blow-up for a system with local and non-local diffusion
Leandro M. Del Pezzo, Raul Ferreira
We study the possibility of non-simultaneous blow-up for positive solutions of a coupled system of two semilinear equations, , , $p, q, α, β>0…
Weak and viscosity solutions for non-homogeneous fractional equations in Orlicz spaces
Maria L. de Borbón, Leandro M. Del Pezzo, Pablo Ochoa
In this paper, we consider non-homogeneous fractional equations in Orlicz spaces, with a source depending on the spatial variable, the unknown function, and its fractional gradient…
Convex and quasiconvex functions in metric graphs
Leandro M. Del Pezzo, Nicolás Frevenza, Julio D. Rossi
We study convex and quasiconvex functions on a metric graph. Given a set of points in the metric graph, we consider the largest convex function below the prescribed datum. We chara…
Fractional convexity
Leandro M. Del Pezzo, Alexander Quaas, Julio D. Rossi
We introduce a notion of fractional convexity that extends naturally the usual notion of convexity in the Euclidean space to a fractional setting. With this notion of fractional co…
Quasiconvex functions on regular trees
Leandro M. Del Pezzo, Nicolas Frevenza, Julio D. Rossi
We introduce a definition of a quasiconvex function on an infinite directed regular tree that depends on what we understood by a segment on the tree. Our definition is based on thi…
Study of the existence of supersolutions for nonlocal equations with gradient terms
Begoña Barrios, Leandro M. Del Pezzo
We study the existence of positive supersolutions of nonlocal equations in exterior domains where the datum can be comparade with near th…
Dirichlet-to-Neumann maps on Trees
Leandro M. Del Pezzo, Nicolás Frevenza, Julio D. Rossi
In this paper we study the Dirichlet-to-Neumann map for solutions to mean value formulas on trees. We give two alternative definition of the Dirichlet-to-Neumann map. For the first…
An optimization problem with volume constraint with applications to optimal mass transport
Joao Vitor da Silva, Leandro M. Del Pezzo, Julio D. Rossi
In this manuscript we study the following optimization problem with volume constraint: \[ \min\left\{\frac{1}{p}\int_Ω |\nabla v|^pdx- \int_{\partial Ω} gv\,dS \colon v \in W^{1, p…
Symmetry results in the half space for a semi-linear fractional Laplace equation through a one-dimensional analysis
B. Barrios, L. Del Pezzo, J. García-Melián +1
In this paper we analyze the semi-linear fractional Laplace equation $$(-Δ)^s u = f(u) \quad\text{ in } \mathbb{R}^N_+,\quad u=0 \quad\text{ in } \mathbb{R}^N\setminus \mathbb{R}^N…
Traces for fractional Sobolev spaces with variable exponents
Leandro M. Del Pezzo, Julio D. Rossi
In this note we prove a trace theorem in fractional spaces with variable exponents. To be more precise, we show that if and $q:\p…
A Hopf's lemma and a strong minimum principle for the fractional -Laplacian
Leandro M. Del Pezzo, Alexander Quaas
Our propose here is to provide a Hopf Lemma and a strong minimum principle for week supersolutions of \[ (-Δ_p)^s u= c(x)|u|^{p-2}u \quad \text{ in } Ω\] where is an open set o…
Non-resonant Fredholm alternative and anti-maximum principle for the fractional Laplacian
Leandro M. Del Pezzo, Alexander Quaas
In this paper we extend two nowadays classical results to a nonlinear Dirichlet problem to equations involving the fractional Laplacian. The first result is a existence in a no…
Monotonicity of solutions for some nonlocal elliptic problems in half-spaces
B. Barrios, L. Del Pezzo, J. Garcia-Melian +1
In this paper we consider classical solutions of the semilinear fractional problem in with in ,…
Eigenvalues for systems of fractional Laplacians
Leandro M. Del Pezzo, Julio D. Rossi
We study the eigenvalue problem for a system of fractional Laplacians, that is, $$ \begin{cases} (-Δ_p)^r u = λ\dfracαp|u|^{α-2}u|v|^β &\text{in } Ω,\vspace{.1cm} (-Δ_p)^s u =…
Finite element approximation for the fractional eigenvalue problem
Juan Pablo Borthagaray, Leandro M. Del Pezzo, Sandra Martínez
The purpose of this work is to study a finite element method for finding solutions to the eigenvalue problem for the fractional Laplacian. We prove that the discrete eigenvalue pro…
Fractional eigenvalue problems that approximate Steklov eigenvalues
Leandro M. Del Pezzo, Julio D. Rossi, Ariel M. Salort
In this paper we analyze possible extensions of the classical Steklov eigenvalue problem to the fractional setting. In particular, we find a nonlocal eigenvalue problem of fraction…
Eigenvalues for a nonlocal pseudo Laplacian
Leandro M. Del Pezzo, Julio D. Rossi
In this paper we study the eigenvalue problems for a nonlocal operator of order that is analogous to the local pseudo Laplacian. We show that there is a sequence of eigenva…
The first nontrivial eigenvalue for a system of Laplacians with Neumann and Dirichlet boundary conditions
Leandro M. Del Pezzo, Julio D. Rossi
We deal with the first eigenvalue for a system of two Laplacians with Dirichlet and Neumann boundary conditions. If $Δ_{p}w=\mbox{div}(|\nabla w|^{p-2}w)$ stands for the La…
An optimal mass transport approach for limits of eigenvalue problems for the fractional -Laplacian
L. M. Del Pezzo, J. D. Rossi, N. Saintier +1
We find interpretation using optimal mass transport theory for eigenvalue problems obtained as limits of the eigenvalue problems for the fractional Laplacian operators as $p\to…
The first non-zero Neumann fractional eigenvalue
Leandro M. Del Pezzo, Ariel M. Salort
In this work we study the asymptotic behavior of the first non-zero Neumann fractional eigenvalue as and as We show that there exists a cons…
The first eigenvalue of the Laplacian on quantum graphs
Leandro M. Del Pezzo, Julio D. Rossi
We study the first eigenvalue of the Laplacian (with ) on a quantum graph with Dirichlet or Kirchoff boundary conditions on the nodes. We find lower and upper bound…