{"paper":{"title":"Asymptotic behavior of solutions to the Helmholtz equations with sign changing coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Hoai-Minh Nguyen","submitted_at":"2012-04-06T17:15:42Z","abstract_excerpt":"This paper is devoted to the study of the behavior of the unique solution $u_\\delta \\in H^{1}_{0}(\\Omega)$, as $\\delta \\to 0$, to the equation \\begin{equation*} \\dive(\\epss_\\delta A \\nabla u_{\\delta}) + k^2 \\epss_0 \\Sigma u_{\\delta} = \\epss_0 f \\mbox{in} \\Omega, \\end{equation*} where $\\Omega$ is a smooth connected bounded open subset of $\\mR^d$ with $d=2$ or 3, $f \\in L^2(\\Omega)$, $k$ is a non-negative constant, $A$ is a uniformly elliptic matrix-valued function, $\\Sigma$ is a real function bounded above and below by positive constants, and $\\epss_\\delta$ is a complex function whose {\\bf the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.1518","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"}