48 citations · 83 across the 7 of their papers we have counts for
9 papers · 1 filter
Existence and global behaviour of solutions of a parabolic problem involving the fractional -Laplacian in porous medium
Loïc Constantin, Jacques Giacomoni, Guillaume Warnault
In this paper, we prove the existence and the uniqueness of a weak and mild solution of the following nonlinear parabolic problem involving the porous -fractional Laplacian: \be…
Asymptotic behavior of blowing-up radial solutions for quasilinear elliptic systems arising in the study of viscous, heat conducting fluids
Ahmed Bachir, Jacques Giacomoni, Guillaume Warnault
In this paper, we deal with the following quasilinear elliptic system involving gradient terms in the form: \begin{center} $\begin{cases} Δ_p u= v^m| \nabla u |^α& \text{in}\quad Ω…
Regularity results for a class of nonlinear fractional Laplacian and singular problems
Rakesh Arora, Jacques Giacomoni, Guillaume Warnault
In this article, we investigate the existence, uniqueness, nonexistence, and regularity of weak solutions to the nonlinear fractional elliptic problem of type (see below) inv…
Doubly nonlinear equation involving -homogeneous operators: local existence, uniqueness and global behaviour
Rakesh Arora, Jacques Giacomoni, Guillaume Warnault
In this work, we investigate the qualitative properties as uniqueness, regularity and stabilization of the weak solution to the nonlinear parabolic problem involving general …
A picone Identity for variable exponent operators and applications
Rakesh Arora, Jacques Giacomoni, Guillaume Warnault
In this work, we establish a new Picone identity for anisotropic quasilinear operators, such as the -Laplacian defined as $\mbox{div}(|\nabla u|^{p(x)-2} \nabla u).$ Our exte…
Biharmonic equation with singular nonlinearity
J. Giacomoni, S. Prashanth, G. Warnault
We consider the following problem: \begin{eqnarray*} ( P)\qquad \displaystyle\left\{\begin{array} {ll} & Δ^2 u = K(x)u^{-α} \quad \mbox{ in }\,Ω, \\ &u> 0\quad \mbox{ in }\,Ω, \;\;…
Quasilinear parabolic problem with -Laplacian: existence, uniqueness of weak solutions and stabilization
Jacques Giacomoni, Sweta Tiwari, Guillaume Warnault
We discuss the existence and uniqueness of the weak solution of the following quasilinear parabolic equation in ; on $(0,T)\times\pa…
The Gel'fand problem for the biharmonic operator
Louis Dupaigne, Olivier Goubet, Guillaume Warnault +1
We study stable solutions of a fourth order nonlinear elliptic equation, both in entire space and in bounded domains.
Entire large solutions for semilinear elliptic equations
Louis Dupaigne, Marius Ghergu, Olivier Goubet +1
We analyze the semilinear elliptic equation , in , with a particular emphasis put on the qualitative study of entire large solutions, t…