3 papers
math.AP2026
New definitions of a solution of a one-dimensional elliptic equation with a singular first order divergence term
Daniela Giachetti, Pedro Jesús MartÃnez-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…
math.AP2024
Unexpected phenomena in a one dimensional elliptic equation with a singular first order divergence term
Daniela Giachetti, Pedro J. MartÃnez-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)…
math.AP2024
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…