{"paper":{"title":"On the electrostatic Born-Infeld equation with extended charges","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessio Pomponio, Denis Bonheure, Pietro d'Avenia","submitted_at":"2015-06-25T07:51:09Z","abstract_excerpt":"In this paper, we deal with the electrostatic Born-Infeld equation \\begin{equation}\\label{eq:BI-abs} \\tag{$\\mathcal{BI}$} \\left\\{ \\begin{array}{ll} -\\operatorname{div}\\left(\\displaystyle\\frac{\\nabla \\phi}{\\sqrt{1-|\\nabla \\phi|^2}}\\right)= \\rho, & \\hbox{in } \\mathbb{R}^N, \\\\ \\displaystyle\\lim_{|x|\\to \\infty}\\phi(x)= 0, \\end{array} \\right. \\end{equation} where $\\rho$ is an assigned extended charge density. We are interested in the existence and uniqueness of the potential $\\phi$ and finiteness of the energy of the electrostatic field $-\\nabla \\phi$. We first relax the problem and treat it with t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.07649","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"}