{"paper":{"title":"Partial Data Calder\\'on Problems for $L^{n/2}$ Potentials on Admissible Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Leo Tzou","submitted_at":"2018-05-22T12:00:35Z","abstract_excerpt":"We solve the partial data Calder\\'on problem on conformally transversallly anisotropic (CTA) manifolds with $L^{n/2}$ potentials - on par with sharp unique continuation result of \\cite{JerKen}. A trivial consequence of this is the sharp regularity improvement to the result of Kenig-Sj\\\"ostrand-Uhlmann \\cite{ksu}. This is done by constructing a \"Green's function\" which possesses both desirable boundary conditions {\\em and} satisfies semiclassical type estimates in the suitable $L^{p}$ spaces. No Carleman estimates were used in the writing of this article which makes it starkly different from th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.09161","kind":"arxiv","version":5},"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"}