{"paper":{"title":"Doubling inequalities for the Lam\\'e system with rough coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ching-Lung Lin, Herbert Koch, Jenn-Nan Wang","submitted_at":"2015-12-17T14:54:08Z","abstract_excerpt":"In this paper we study the local behavior of a solution to the Lam\\'e system when the Lam\\'e coefficients $\\lambda$ and $\\mu$ satisfy that $\\mu$ is Lipschitz and $\\lambda$ is essentially bounded in dimension $n\\ge 2$. One of the main results is the \\emph{local} doubling inequality for the solution of the Lam\\'e system. This is a quantitative estimate of the strong unique continuation property. Our proof relies on Carleman estimates with carefully chosen weights. Furthermore, we also prove the \\emph{global} doubling inequality, which is useful in some inverse problems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.05613","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"}