Laurent V'eron

activity

20142023

most citedAn elliptic semilinear equation with source term and boundary measure data: the supercritical case

23 citations · 37 across the 8 of their papers we have counts for

collaborators

10 papers

math.AP2023★ 1 cited

The Cauchy problem associated to the logarithmic Laplacian with an application to the fundamental solution

Huyuan Chen, Laurent Véron

Let $\lnlap$ be the logarithmic Laplacian operator with Fourier symbol $2 ln ∣ ζ ∣$ , we study the expression of the diffusion kernel which is associated to the equation $$\partial_tu…

math.AP2023

Local behaviour of the solutions of the Chipot-Weissler equation

Marie-Françoise Bidaut-Véron, Laurent Véron

We study the local properties of positive solutions of the equation $- Δ u = u^{p} - m ∣\nabla u ∣^{q}$ in a punctured domain $Ω ∖ {0}$ of $R^{N}$ or in a exterior domain $\math…

math.AP2022

Singularities of fractional Emden's equations via Caffarelli-Silvestre extension

Huyuan Chen, Laurent Véron

We study the isolated singularities of functions satisfying (E) (-- $Δ$ ) s v $\pm$ |v| p--1 v = 0 in $Ω$ \{0}, v = 0 in R N $Ω $, w h er e 0 < s < 1, p > 1 an d$ Ω$ is a bounded domain con…

math.AP2022

Trace and boundary singularities of positive solutions of a class of quasilinear equations

Marie-Françoise Bidaut-Véron, Laurent Véron

We study properties of positive functions satisfying (E) -- $Δ$ u+m| $\nabla$ u| q -- u p = 0 is a domain $Ω$ or in R N + when p > 1 and 1 < q < 2. We give sufficient conditions for th…

math.AP2021

Singular solutions of some elliptic equations involving mixed absorption-reaction

Marie-Françoise Bidaut-Véron, Marta Garcia Huidobro, Laurent Véron

We study properties of nonnegative functions satisfying (E) $- Δ u + u^{p} - M ∣\nabla u ∣^{q} = 0$ is a domain of $R^{N}$ when $p > 1$ , $M > 0$ and $1 < q < p$ . We concentrate our analysis on t…

math.AP2018

Quasilinear elliptic equations with a source reaction term involving the function and its gradient and measure data

Marie-Françoise Bidaut-Véron, Quoc-Hung Nguyen, Laurent Veron

We study the equation --div(A(x, u)) = g(x, u, u) + $μ$ where $μ$ is a measure and either g(x, u, u) $\sim$ |u| q 1 u||u| q 2 or g(x, u, u) $\sim$ |u| s 1 u + ||u| s 2. We give suf…

math.AP2017

The spherical p-harmonic eigenvalue problem in non-smooth domains

Konstantinos Gkikas, Laurent Véron

We prove the existence of p-harmonic functions under the form u(r, $σ$ ) = r -- $β$ $ω$ ( $σ$ ) in any cone C S generated by a spherical domain S and vanishing on $\partial$ C S. We prov…

math.AP2015

Admissible initial growth for diffusion equations with weakly superlinear absorption

Andrey Shishkov, Laurent Véron

We study the admissible growth at infinity of initial data of positive solutions of $\prt\_t u-\Gd u+f(u)=0$ in $\BBR\_+\ti\BBR^N$ when $f (u)$ is a continuous function, {\it mildly…

math.AP2014★ 23 cited

An elliptic semilinear equation with source term and boundary measure data: the supercritical case

Marie-Françoise Bidaut-Véron, Giang Hoang, Quoc-Hung Nguyen +1

We give new criteria for the existence of weak solutions to an equation with a super linear source term \begin{align*}-Δu = u^q ~~\text{in}~Ω,~~u=σ~~\text{on }~\partialΩ\end{align*…

math.AP2014★ 13 cited

Elliptic equations involving general subcritical source nonlinearity and measures

Huyuan Chen, Patricio Felmer, Laurent Véron

In this article, we study the existence of positive solutions to elliptic equation (E1) $(- Δ)^{α} u = g (u) + σ ν in Ω,$ subject to the condition (E2) $$u=\varrhoμ\quad {\r…