106 citations · 620 across the 36 of their papers we have counts for
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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,\\…