46 citations · 96 across the 8 of their papers we have counts for
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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…
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)…
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 $…
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 $$ \begin{cases} \displaystyle -Δ_1 u = g(u)|D u|+h(u)f & \text{in…
The Dirichlet problem for singular elliptic equations with general nonlinearities
Virginia De Cicco, Daniela Giachetti, Francescantonio Oliva +1
In this paper, under very general assumptions, we prove existence and regularity of distributional solutions to homogeneous Dirichlet problems of the form $$\begin{cases} \displays…
Homogenization of a Dirichlet semilinear elliptic problem with a strong singularity at in a domain with many small holes
Daniela Giachetti, Pedro J. Martínez-Aparicio, François Murat
We perform the homogenization of the semilinear elliptic problem \begin{equation*} \begin{cases} u^\varepsilon \geq 0 & \mbox{in} \; Ω^\varepsilon,\\ \displaystyle - div \,A(x) D u…
Definition, existence, stability and uniqueness of the solution to a semilinear elliptic problem with a strong singularity at
Daniela Giachetti, Pedro J. Martínez-Aparicio, François Murat
In this paper we consider a semilinear elliptic equation with a strong singularity at , namely $ \displaystyle u\geq 0 \mbox{ in } Ω$, $ \displaystyle - div \,A(x) D u = F(x,u…
A semilinear elliptic equation with a mild singularity at : existence and homogenization
Daniela Giachetti, Pedro J. Martínez-Aparicio, François Murat
In this paper we consider semilinear elliptic equations with singularities, whose prototype is the following \begin{equation*} \begin{cases} \displaystyle - div \,A(x) D u = f(x)g(…