{"paper":{"title":"A \"milder\" version of Calder\\'on's inverse problem for anisotropic conductivities and partial data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"El Maati Ouhabaz (IMB)","submitted_at":"2015-01-29T07:47:07Z","abstract_excerpt":"Given  a general symmetric elliptic operator $$ L\\_{a} := \\sum\\_{k,,j=1}^d \\p\\_k (a\\_{kj} \\p\\_j) + \\sum\\_{k=1}^d a\\_k \\p\\_k - \\p\\_k(\\overline{a\\_k} .) + a\\_0$$we define the associated Dirichlet-to-Neumann (D-t-N) operator with  partial data, i.e.,  data supported in a part of the boundary. We prove positivity, $L^p$-estimates  and domination properties for the semigroup associated with this D-t-N operator. Given $L\\_a $ and $L\\_b$ of the previous type with bounded measurable coefficients $a = \\{a\\_{kj}, \\ a\\_k, a\\_0 \\}$ and $b = \\{b\\_{kj}, \\ b\\_k, b\\_0 \\}$, we prove that if  their  partial D-t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.07364","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"}