{"paper":{"title":"The $L^p$ Carleman estimate and a partial data inverse problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Francis J. Chung, Leo Tzou","submitted_at":"2016-10-06T02:02:52Z","abstract_excerpt":"We construct an explicit Green's function for the conjugated Laplacian $e^{-\\omega \\cdot x/h}\\Delta e^{-\\omega \\cdot x/h}$, which let us control our solutions on roughly half of the boundary. We apply the Green's function to solve a partial data inverse problem for the Schr\\\"odinger equation with potential $q \\in L^{n/2}$. We also use this Green's function to derive $L^p$ Carleman estimates similar to the ones in Kenig-Ruiz-Sogge \\cite{krs}, but for functions with support up to part of the boundary."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.01715","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"}