{"paper":{"title":"Weyl formula for the negative dissipative eigenvalues of Maxwell's equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Ferruccio Colombini, Vesselin Petkov","submitted_at":"2017-05-26T13:37:21Z","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 study the case when $\\Omega = \\{x \\in {\\mathbb R^3}:\\: |x| > 1\\}$ and $\\gamma \\neq 1$ is a constant. We establish a Weyl formula for the counting function of the negative real eigenvalues of $G_b.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09583","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"}