{"paper":{"title":"The Brezis-Nirenberg problem for the curl-curl operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jaros{\\l}aw Mederski","submitted_at":"2016-09-13T19:30:48Z","abstract_excerpt":"We look for solutions $E:\\Omega\\to\\mathbb{R}^3$ of the problem $$ \\left\\{ \\begin{aligned} &\\nabla\\times(\\nabla\\times E) +\\lambda E = |E|^{p-2}E &&\\quad \\text{in }\\Omega &\\nu\\times E = 0 &&\\quad \\text{on }\\partial\\Omega \\end{aligned} \\right. $$ on a bounded Lipschitz domain $\\Omega\\subset\\mathbb{R}^3$, where $\\nabla\\times$ denotes the curl operator in $\\mathbb{R}^3$. The equation describes the propagation of the time-harmonic electric field $\\Re\\{E(x)e^{i\\omega t}\\}$ in a nonlinear isotropic material $\\Omega$ with $\\lambda=-\\mu \\varepsilon \\omega^2\\leq 0$, where $\\mu$ and $\\varepsilon$ stand fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03989","kind":"arxiv","version":4},"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"}