{"paper":{"title":"Eigenvalues for Maxwell's equations with dissipative boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Ferruccio Colombini, Jeffrey Rauch, Vesselin Petkov","submitted_at":"2015-06-08T15:35:27Z","abstract_excerpt":"Let $V(t) = e^{tG_b},\\: t \\geq 0,$ be the semigroup generated by Maxwell's equations in an exterior domain $\\Omega \\subset {\\mathbb R}^3$ with dissipative boundary condition $E_{tan}- \\gamma(x) (\\nu \\wedge B_{tan}) = 0, \\gamma(x) > 0, \\forall x \\in \\Gamma = \\partial \\Omega.$ We prove that if $\\gamma(x)$ is nowhere equal to 1, then for every $0 < \\epsilon \\ll 1$ and every $N \\in {\\mathbb N}$ the eigenvalues of $G_b$ lie in the region $\\Lambda_{\\epsilon} \\cup {\\mathcal R}_N,$ where $\\Lambda_{\\epsilon} = \\{ z \\in {\\mathbb C}:\\: |\\Re z | \\leq C_{\\epsilon} (|\\Im z|^{\\frac{1}{2} + \\epsilon} + 1), \\:"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.02555","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"}