{"paper":{"title":"Energy concentration and explicit Sommerfeld radiation condition for the electromagnetic Helmholtz equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Miren Zubeldia","submitted_at":"2012-01-02T16:55:19Z","abstract_excerpt":"We study the electromagnetic Helmholtz equation \n\\notag (\\nabla + ib(x))^{2}u(x) + n(x)u(x) = f(x), \\quad x\\in\\Rd\nwith the magnetic vector potential $b(x)$ and $n(x)$ a variable index of refraction that does not necessarily converge to a constant at infinity, but can have an angular dependency like $n(x) \\to n_{\\infty}(\\frac{x}{|x|})$ as $|x|\\to\\infty$. We prove an explicit Sommerfeld radiation condition\n\\notag \\int_{\\Rd} |\\D u - in_{\\infty}^{1/2}\\frac{x}{|x|}u|^{2} \\frac{dx}{1+|x)} < + \\infty\nfor solutions obtained from the limiting absorption principle and we also give a new energy estimate\n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.0494","kind":"arxiv","version":2},"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"}