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Equilibrium measures and equilibrium potentials in the Born-Infeld model
Denis Bonheure, Pietro d'Avenia, Alessio Pomponio +1
In this paper, we consider the electrostatic Born-Infeld model \begin{equation*} \tag{} \left\{ \begin{array}{rcll} -\operatorname{div}\left(\displaystyle\frac{\nabla…
Periodic solutions and torsional instability in a nonlinear nonlocal plate equation
Denis Bonheure, Filippo Gazzola, Ederson Moreira dos Santos
A thin and narrow rectangular plate having the two short edges hinged and the two long edges free is considered. A nonlinear nonlocal evolution equation describing the deformation…
Singular radial solutions for the Keller-Segel equation in high dimension
Denis Bonheure, Jean-Baptiste Casteras, Juraj Foldes
We study singular radially symmetric solution of the stationary Keller-Segel equation, that is, an elliptic equation with exponential nonlinearity, which is super-critical in dimen…
On the regularity of the minimizer of the electrostatic Born-Infeld energy
Denis Bonheure, Alessandro Iacopetti
We consider the electrostatic Born-Infeld energy \begin{equation*} \int_{\mathbb{R}^N}\left(1-{\sqrt{1-|\nabla u|^2}}\right)\, dx -\int_{\mathbb{R}^N}ρu\, dx, \end{equation*} where…
On a fourth order nonlinear Helmholtz equation
Denis Bonheure, Jean-Baptiste Casteras, Rainer Mandel
In this paper, we study the mixed dispersion fourth order nonlinear Helmholtz equation in for positive, bounded and -peri…
Normalized solutions to the mixed dispersion nonlinear Schrödinger equation in the mass critical and supercritical regime
Denis Bonheure, Jean-Baptiste Casteras, Tianxiang Gou +1
In this paper, we study the existence of solutions to the mixed dispersion nonlinear Schrödinger equation under the constr…