{"paper":{"title":"Limit solutions of the Chern-Simons equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Adilson E. Presoto, Augusto C. Ponce","submitted_at":"2012-09-07T14:46:46Z","abstract_excerpt":"We investigate the scalar Chern-Simons equation $-\\Delta u + e^u(e^u-1) = \\mu$ in cases where there is no solution for a given nonnegative finite measure $\\mu$. Approximating $\\mu$ by a sequence of nonnegative $L^1$ functions or finite measures for which this equation has a solution, we show that the sequence of solutions of the Dirichlet problem converges to the solution with largest possible datum $\\mu^# \\le \\mu$ and we derive an explicit formula of $\\mu^#$ in terms of $\\mu$. The counterpart for the Chern-Simons system with datum $(\\mu, \\nu)$ behaves differently and the conclusion depends on"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1556","kind":"arxiv","version":1},"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"}