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We work with general functionals of the form $\\sigma|\\nabla u|^p$, $0 < p \\leq 1$, where $u$ is the solution of the elliptic partial differential equation $\\nabla\\cdot \\sigma \\nabla u =0$ on a bounded domain $\\Omega$ with boundary conditions $u|_{\\partial \\Omega} = f$. We prove stability of the linearization and H\\\"older conditional stability for the non-linear problem of recovering $\\sigma$ from the internal measurement."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1306.1978","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-09T04:18:24Z","cross_cats_sorted":[],"title_canon_sha256":"234004d5c1e50f151cd181a945b94235ff17632beb04bf879f005f7f75a08f86","abstract_canon_sha256":"e3571421344bd4c67acf2818b11b6583ad797fd3989f2e1107f29e940384b256"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:49:24.609500Z","signature_b64":"77AUPVHQFupZaVpmjUDemKXgE693V8yEKyVdomCT01WUSkTAX38NufvUS4bgQjztNElFJ6cgM4AfoZYab/fBCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"24568eea9c14bc069e7aac461647c86d05bba994d2cf7b46bcb3ce8935905f4e","last_reissued_at":"2026-05-18T01:49:24.608794Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:49:24.608794Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stability of Coupled-Physics Inverse Problems with internal measurements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Carlos Montalto, Plamen Stefanov","submitted_at":"2013-06-09T04:18:24Z","abstract_excerpt":"In this paper, we develop a general approach to prove stability for the non linear second step of hybrid inverse problems. 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