81 citations · 239 across the 24 of their papers we have counts for
27 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…
Optimal insulation and concentration breaking for nonlinear Robin boundary value problems
Francesco Della Pietra, Francescantonio Oliva
We consider an optimal insulation problem for a bounded domain in driven by the -Laplace operator (). We model the convective heat transfer between the body…
Existence and uniqueness of weak solutions to singular anisotropic elliptic problems
Francesco Esposito, Francescantonio Oliva, Eugenio Vecchi
In this paper we consider a quasilinear singular anisotropic elliptic problem with a p-sublinear perturbation. We prove uniqueness of weak solutions and we provide necessary and su…
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(…
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…
Some remarks on optimal insulation with Robin boundary conditions
Francesco Della Pietra, Francescantonio Oliva
We consider an optimal insulation problem of a given domain in . We study a model of heat trasfer determined by convection; this corresponds, before insulation, to a R…
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 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 $$ \begin{cases} - {\rm div}\left(|u|^m\frac{D u}{|D u|}\right) = f & \text{in}\;Ω,\\ \newline…
Optimal global regularity for 1-Laplace type BVP's with singular lower order terms
Antonio J. Martínez Aparicio, Francescantonio Oliva, Francesco Petitta
In this paper we provide a complete characterization of the regularity properties of the solutions associated to the homogeneous Dirichlet problem \begin{equation*} \begin{cases} \…
Finite energy solutions for nonlinear elliptic equations with competing gradient, singular and terms
Francesco Balducci, Francescantonio Oliva, Francesco Petitta
In this paper we deal with the following boundary value problem \begin{equation*} \begin{cases} -Δ_{p}u + g(u) | \nabla u|^{p} = h(u)f & \text{in ,} \newline u\geq 0 & \text{in…
The role of absorption terms in Dirichlet problems for the prescribed mean curvature equation
Francescantonio Oliva, Francesco Petitta, Sergio Segura de León
In this paper we study existence and uniqueness of solutions to Dirichlet problems as $$ \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 $…
On a nonlinear Robin problem with an absorption term on the boundary and data
Francesco Della Pietra, Francescantonio Oliva, Sergio Segura de León
We deal with existence and uniqueness of nonnegative solutions to \begin{equation*} \left\{ \begin{array}{l} -Δu = f(x) \text{ in }Ω, \frac{\partial u}{\partial ν} + λ(x) u = \frac…
Behaviour of solutions to -Laplacian with Robin boundary conditions as goes to
Francesco Della Pietra, Francescantonio Oliva, Sergio Segura de León
We study the asymptotic behaviour, as , of the solutions of the following inhomogeneous Robin boundary value problem: \begin{equation} \label{pbabstract} \tag{P} \left\…
The Dirichlet problem for possibly singular elliptic equations with degenerate coercivity
Riccardo Durastanti, Francescantonio Oliva
We deal with existence, uniqueness and regularity of nonnegative solutions to a Dirichlet problem for equations as \begin{equation*} \displaystyle -\operatorname{div}\left(\frac{|\…
On some parabolic equations involving superlinear singular gradient terms
Martina Magliocca, Francescantonio Oliva
In this paper we prove existence of nonnegative solutions to parabolic Cauchy-Dirichlet problems with superlinear gradient terms which are possibly singular. The model equation is…
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: $$ \left\{\begin{array}{ll} \displaystyle -Δ_1 u =h(u)f(x)&\…
Comparison principle for elliptic equations with mixed singular nonlinearities
Riccardo Durastanti, Francescantonio Oliva
We deal with existence and uniqueness of positive solutions of an elliptic boundary value problem modeled by \begin{equation*} \begin{cases} \displaystyle -Δ_p u= \frac{f}{u^γ} + g…
1-Laplacian type problems with strongly singular nonlinearities and gradient terms
Daniela Giachetti, Francescantonio Oliva, Francesco Petitta
We show optimal existence, nonexistence and regularity results for nonnegative solutions to Dirichlet problems as $$ \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…
Radial symmetry for a quasilinear elliptic equation with a critical Sobolev growth and Hardy potential
Francescantonio Oliva, Berardino Sciunzi, Giusi Vaira
We consider weak positive solutions to the critical -Laplace equation with Hardy potential in where , $0\le γ<\l…
Regularizing effect of absorption terms in singular problems
Francescantonio Oliva
We prove existence of solutions to problems whose model is $$\begin{cases} \displaystyle -Δ_p u + u^q = \frac{f}{u^γ} & \text{in}\ Ω, \newline u\ge0 &\text{in}\ Ω,\newline u=0 &\te…
The Dirichlet problem for singular elliptic equations with general nonlinearities
Virginia De Cicco, Daniela Giachetti, Francescantonio Oliva +1
In this paper, under very general assumptions, we prove existence and regularity of distributional solutions to homogeneous Dirichlet problems of the form $$\begin{cases} \displays…