{"paper":{"title":"Spectral properties of the Neumann-Poincar\\'e operator and uniformity of estimates for the conductivity equation with complex coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hyeonbae Kang, Hyundae Lee, Jaemin Shin, Kyoungsun Kim, Sanghyeon Yu","submitted_at":"2014-06-16T00:25:41Z","abstract_excerpt":"We consider well-posedness of the boundary value problem in presence of an inclusion with complex conductivity $k$. We first consider the transmission problem in $\\mathbb{R}^d$ and characterize solvability of the problem in terms of the spectrum of the Neumann-Poincar\\'e operator. We then deal with the boundary value problem and show that the solution is bounded in its $H^1$-norm uniformly in $k$ as long as $k$ is at some distance from a closed interval in the negative real axis. We then show with an estimate that the solution depends on $k$ in its $H^1$-norm Lipschitz continuously. We finally"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3873","kind":"arxiv","version":3},"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"}