13 citations · 13 across the 2 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)…
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…