{"paper":{"title":"On the regularity of the minimizer of the electrostatic Born-Infeld energy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessandro Iacopetti, Denis Bonheure","submitted_at":"2018-04-06T16:56:04Z","abstract_excerpt":"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}\\rho u\\, dx, \\end{equation*} where $\\rho \\in L^{m}(\\mathbb{R}^N)$ is an assigned charge density, $m \\in [1,2_*]$, $2_*:=\\frac{2N}{N+2}$, $N\\geq 3$. We prove that if $\\rho \\in L^q(\\mathbb{R}^N) $ for $q>2N$, the unique minimizer $u_\\rho$ is of class $W_{loc}^{2,2}(\\mathbb{R}^N)$. Moreover, if the norm of $\\rho$ is sufficiently small, the minimizer is a weak solution of the associated PDE\n  \\begin{equation}\\label{eq:BI-abs} \\tag{$\\mathcal{BI}$} -\\o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.02355","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}