On the Electrostatic Born–Infeld Equation with Extended Charges

@article{Bonheure2015OnTE,
  title={On the Electrostatic Born–Infeld Equation with Extended Charges},
  author={D. Bonheure and P. d'Avenia and A. Pomponio},
  journal={Communications in Mathematical Physics},
  year={2015},
  volume={346},
  pages={877-906}
}
AbstractIn this paper, we deal with the electrostatic Born–Infeld equation $$\left\{\begin{array}{ll}-\operatorname{div} \left(\displaystyle\frac{\nabla\phi}{\sqrt{1-|\nabla \phi|^2}} \right)= \rho \quad{in} \mathbb{R}^N, \\ \displaystyle\lim_{|x|\to \infty} \phi(x)= 0,\end{array}\right. \quad \quad \quad \quad ({\mathcal{BI}})$$-div∇ϕ1-|∇ϕ|2=ρinRN,lim|x|→∞ϕ(x)=0,(BI)where $${\rho}$$ρ is an assigned extended charge density. We are interested in the existence and uniqueness of the potential… Expand
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