Searcharxiv⌕ Search

arXiv subjects

Olivier Guibé

Publications and source records attributed to Olivier Guibé.

7 recordsLinked to original sources
arXiv2022

Finite volume scheme and renormalized solutions for nonlinear elliptic Neumann problem with L1 data

In this paper we study the convergence of a finite volume approximation of a convective diffusive elliptic problem with Neumann boundary conditions and L 1 data. To deal with the non-coercive character of the equation and the low regularity of the right hand-side we mix the finite volume tools and the renormalized techniques. To handle the Neumann boundary conditions we choose solutions having a null median and we prove a convergence result.

math.AP↗
arXiv2017

Uniqueness for Neumann problems for nonlinear elliptic equations

In the present paper we prove uniqueness results for solutions to a class of Neumann boundary value problems whose prototype is --div((1 + |$\nabla$u| 2) (p--2)/2 $\nabla$u) -- div(c(x)|u| p--2 u) = f in $Ω$, (1 + |$\nabla$u| 2) (p--2)/2 $\nabla$u + c(x)|u| p--2 u $\times$ n = 0 on $\partial$$Ω$,

math.AP↗
arXiv2014

Neumann problems for nonlinear elliptic equations with $L^1$ data

In the present paper we prove existence results for solutions to nonlinear elliptic Neumann problems whose prototype is \begin{equation*} \begin{cases} -Δ_{p} u -\text{div} (c(x)|u|^{p-2}u)) =f & \text{in}\ Ω, \\ \left( |\nabla u|^{p-2}\nabla u+ c(x)|u|^{p-2}u \right)\cdot\underline n=0 & \text{on}\ \partial Ω\,, \end{cases} \end{equation*} when $f$ is just a summable function. Our approach allows also to deduce a stability result for renormalized solutions and an existence result for operator with a zero order term.

math.AP↗
arXiv2008

Nonlinear and non-coercive elliptic problems with integrable data

In this paper we study existence and uniqueness of renormalized solution to the following problem $λ(x,u) -div a(x,Du) +Φ(x,u)) =f$ with $f$ in $L^1$ and with Dirichlet-Neumann boundary condition. The main difficulty in this task is that in general the operator entering in the above equation is not coercive in a Sobolev space. Moreover, the possible degenerate character of $λ$ with respect to $u$ renders more complex the proof of uniqueness for integrable data $f$.

math.AP↗
arXiv2008

Existence and uniqueness results for a nonlinear stationary system

We prove a few existence results of a solution for a static system with a coupling of thermoviscoelastic type. As this system involves $L^1$ coupling terms we use the techniques of renormalized solutions for elliptic equations with $L^1$ data. We also prove partial uniqueness results.

math.AP↗