{"paper":{"title":"Global Calderon-Zygmund estimates for irregular double-phase evolution problem with non-divergence data","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Rakesh Arora, Sergey Shmarev","submitted_at":"2026-07-05T20:36:53Z","abstract_excerpt":"We study irregular double-phase parabolic equations with variable exponents and non-divergence data, \\[ u_t-\\operatorname{div} \\left(\\mathcal{F}(z,\\nabla u)\\nabla u \\right)=f(z),\\quad z=(x,t)\\in Q_T:=\\Omega\\times (0,T), \\]\n  under the homogeneous Dirichlet boundary conditions. Here, $\\Omega \\subset \\mathbb{R}^N$, $N \\geq 2$, is a bounded domain, $T>0$, \\[ \\mathcal{F}(z,\\nabla u)=a(z)|\\nabla u|^{p(z)-2} + b(z) |\\nabla u |^{q(z)-2} \\] with given Lipschitz-continuous exponents $p,q$ that satisfy a suitable balance condition. The nonnegative coefficients $a(z), b(z)$ satisfy the inequality $a(z)+b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.04492","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/2607.04492/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"}