106 citations · 620 across the 36 of their papers we have counts for
40 papers
Existence and classification of solutions for singular 1-Laplacian equations with gradient terms
Antonio J. Martínez Aparicio, Francescantonio Oliva, Francesco Petitta
We study the existence and qualitative properties of non-negative solutions to singular 1-Laplacian problems of the form \begin{equation*} \begin{cases} -Δ_1 u = g(u)|D u| + h(u)f…
Sharp existence and non-existence for singular -Laplace equations with Hardy potentials
Juan Carlos Chata Ortiz, Francesco Petitta
In this paper, we investigate the singular Dirichlet problem \begin{equation}\label{abs1} \left\{ \begin{array}{rclr} -Δ_1u &=&\dfracλ{|x|}\hbox{Sgn}\,(u)+\dfrac{f}{u^γ}&\quad\mbox…
Gradient constraints, Born-Infeld, and maximal surfaces via superposition of infinitely many -Laplacians
Haydar Abdel Hamid, Juan Carlos Chata Ortiz, Francesco Petitta +1
We study the Dirichlet problem for an infinite series of -Laplacians, where $\{a_{p}\}…
New definitions of a solution of a one-dimensional elliptic equation with a singular first order divergence term
Daniela Giachetti, Pedro Jesús Martínez-Aparicio, François Murat +1
In this paper, which is a continuation of our recent paper [1], we give two new definitions of a weak solution of the one-dimensional, elliptic, nonlinear singular problem which is…
Existence and non-existence phenomena for nonlinear elliptic equations with data and singular reactions
Francescantonio Oliva, Francesco Petitta, Matheus F. Stapenhorst
We study existence and non-existence of solutions for singular elliptic boundary value problems as \begin{equation}\label{eintro}\begin{cases}\tag{1} \displaystyle -Δ_p u+ \frac{a(…
Quasilinear elliptic equations with singular quadratic growth terms
Lucio Boccardo, Tommaso Leonori, Luigi Orsina +1
In this paper we deal with positive solutions for singular quasilinear problems whose model is $$ \begin{cases} -Δu + \frac{|\nabla u|^2}{(1-u)^γ}=g & \mbox{in ,}\newline \hfill…
A duality approach to the fractional Laplacian with measure data
Kenneth H. Karlsen, Francesco Petitta, Suleyman Ulusoy
We describe a duality method to prove both existence and uniqueness of solutions to nonlocal problems like with vanishing condition…
Diffuse measures and nonlinear parabolic equations
Francesco Petitta, Augusto C. Ponce, Alessio Porretta
Given a parabolic cylinder , where is a bounded domain, we prove new properties of solutions of \[ u_t-Δ_p u = μ\quad \text{in } \] wi…
Existence and nonexistence of solutions for singular quadratic quasilinear equations
David Arcoya, José Carmona, Tommaso Leonori +3
We study both existence and nonexistence of nonnegative solutions for nonlinear elliptic problems with singular lower order terms that have natural growth with respect to the gradi…
Global existence for a Leibenson type equation with reaction on Riemannian manifolds
Giulia Meglioli, Francescantonio Oliva, Francesco Petitta
We show a global existence result for a doubly nonlinear porous medium type equation of the form on a complete and non-compact Riemannian manifold of…
The Sattinger iteration method for 1-Laplace type problems and its application to concave-convex nonlinearities
Antonio J. Martínez Aparicio, Francescantonio Oliva, Francesco Petitta
In this paper we extend the classical sub-supersolution Sattinger iteration method to -Laplace type boundary value problems of the form \begin{equation*} \begin{cases} \displays…
Singular Elliptic PDEs: an extensive overview
Francescantonio Oliva, Francesco Petitta
In this survey we provide an overview of nonlinear elliptic homogeneous boundary value problems featuring singular zero-order terms with respect to the unknown variable whose proto…
Existence, non-existence and degeneracy of limit solutions to -Laplace problems involving Hardy potentials as . The case of a critical drift
Juan Carlos Ortiz Chata, Francesco Petitta
In this paper we analyze the asymptotic behaviour as of solutions to $$ \left\{ \begin{array}{rclr} -Δ_pu&=&λ|\nabla u|^{p-2}\nabla u\cdot\frac{x}{|x|^2}+ f&\quad…
Existence and regularity of solutions for the elliptic nonlinear transparent media equation
Francesco Balducci, Francescantonio Oliva, Francesco Petitta +1
In this paper we study existence and regularity of solutions to Dirichlet problems as $$ \begin{cases} - {\rm div}\left(|u|^m\frac{D u}{|D u|}\right) = f & \text{in}\;Ω,\\ \newline…
Unexpected phenomena in a one dimensional elliptic equation with a singular first order divergence term
Daniela Giachetti, Pedro J. Martínez-Aparicio, François Murat +1
We study existence of a weak solution for one-dimensional problems as \begin{equation}\label{intro}\tag{1} \begin{cases} \displaystyle -\frac{d}{dx}\left(a(x) \frac{d u}{dx}\right)…
Optimal global regularity for 1-Laplace type BVP's with singular lower order terms
Antonio J. Martínez Aparicio, Francescantonio Oliva, Francesco Petitta
In this paper we provide a complete characterization of the regularity properties of the solutions associated to the homogeneous Dirichlet problem \begin{equation*} \begin{cases} \…
Existence, non-existence and degeneracy of limit solutions to Laplace problems involving Hardy potentials as
Juan Carlos Ortiz Chata, Francesco Petitta
In this paper we analyze the asymptotic behaviour as of solutions to $$ \left\{ \begin{array}{rclr} -Δ_p u_p&=&\fracλ{|x|^p}|u_p|^{p-2}u_p+f&\quad \mbox{ in } Ω,\\…
Finite energy solutions for nonlinear elliptic equations with competing gradient, singular and terms
Francesco Balducci, Francescantonio Oliva, Francesco Petitta
In this paper we deal with the following boundary value problem \begin{equation*} \begin{cases} -Δ_{p}u + g(u) | \nabla u|^{p} = h(u)f & \text{in ,} \newline u\geq 0 & \text{in…
The role of absorption terms in Dirichlet problems for the prescribed mean curvature equation
Francescantonio Oliva, Francesco Petitta, Sergio Segura de León
In this paper we study existence and uniqueness of solutions to Dirichlet problems as $$ \begin{cases} g(u) -{\rm div}\left(\frac{D u}{\sqrt{1+|D u|^2}}\right) = f & \text{in}\;Ω,\…
Bounded solutions for non-parametric mean curvature problems with nonlinear terms
Daniela Giachetti, Francescantonio Oliva, Francesco Petitta
In this paper we prove existence of nonnegative bounded solutions for the non-autonomous prescribed mean curvature problem in non-parametric form on an open bounded domain of $…
Nonlinear diffusion in transparent media
Lorenzo Giacomelli, Salvador Moll, Francesco Petitta
We consider a prototypical nonlinear parabolic equation whose flux has three distinguished features: it is nonlinear with respect to both the unknown and its gradient, it is homoge…
The Dirichlet problem for the -Laplacian with a general singular term and -data
Marta Latorre, Francescantonio Oliva, Francesco Petitta +1
We study the Dirichlet problem for an elliptic equation involving the -Laplace operator and a reaction term, namely: $$ \left\{\begin{array}{ll} \displaystyle -Δ_1 u =h(u)f(x)&\…
1-Laplacian type problems with strongly singular nonlinearities and gradient terms
Daniela Giachetti, Francescantonio Oliva, Francesco Petitta
We show optimal existence, nonexistence and regularity results for nonnegative solutions to Dirichlet problems as $$ \begin{cases} \displaystyle -Δ_1 u = g(u)|D u|+h(u)f & \text{in…
A nonlinear parabolic problem with singular terms and nonregular data
Francescantonio Oliva, Francesco Petitta
We study existence of nonnegative solutions to a nonlinear parabolic boundary value problem with a general singular lower order term and a nonnegative measure as nonhomogeneous dat…