{"paper":{"title":"Reconstruction of coefficients in the double phase problem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"C\\u{a}t\\u{a}lin I. C\\^arstea, Philipp Zimmermann","submitted_at":"2025-04-02T12:44:48Z","abstract_excerpt":"The main purpose of this article is to reconstruct the nonnegative coefficient $a$ in the double phase problem $\\mathrm{div}\\,(|\\nabla u|^{p-2}\\nabla u+a|\\nabla u|^{q-2}\\nabla u)=0$ in a domain $\\Omega$, $u=f$ on $\\partial\\Omega$, from the Dirichlet to Neumann (DN) map $\\Lambda_a$. We show that this can be achieved, when the coefficient $a$ has H\\\"older continuous first order derivatives and the exponents satisfy $1<p\\neq q<\\infty$. Our reconstruction method relies on a careful analysis of the asymptotic behavior of the solution $u$ to the double phase problem with small or large Dirichlet dat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.01691","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.01691/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}