{"paper":{"title":"Nonlinear time-harmonic Maxwell equations in domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Jaros{\\l}aw Mederski, Thomas Bartsch","submitted_at":"2016-10-20T09:32:57Z","abstract_excerpt":"The search for time-harmonic solutions of nonlinear Maxwell equations in the absence of charges and currents leads to the elliptic equation $$\\nabla\\times\\left(\\mu(x)^{-1} \\nabla\\times u\\right) - \\omega^2\\varepsilon(x)u = f(x,u)$$ for the field $u:\\Omega\\to\\mathbb{R}^3$ in a domain $\\Omega\\subset\\mathbb{R}^3$. Here $\\varepsilon(x) \\in \\mathbb{R}^{3\\times3}$ is the (linear) permittivity tensor of the material, and $\\mu(x) \\in \\mathbb{R}^{3\\times3}$ denotes the magnetic permeability tensor. The nonlinearity $f:\\Omega\\times\\mathbb{R}^3\\to\\mathbb{R}^3$ comes from the nonlinear polarization. If $f="},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06338","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"}