{"paper":{"title":"Very weak solutions of subquadratic parabolic systems with non-standard $p(x,t)$-growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Qifan Li","submitted_at":"2016-11-04T15:26:15Z","abstract_excerpt":"The aim of this paper is to establish a higher integrability result for very weak solutions of certain parabolic systems whose model is the parabolic $p(x,t)$-Laplacian system. Under assumptions on the exponent function $p:\\Omega_T=\\Omega\\times (0,T)\\to\\left(\\frac{2n}{n+2},2\\right]$, it is shown that any very weak solution $u:\\Omega_T\\rightarrow\\mathbb{R}^N$ with $|Du|^{p(\\cdot)(1-\\varepsilon)}\\in L^1(\\Omega_T)$ belongs to the natural energy spaces, i.e. $|Du|^{p(\\cdot)}\\in L^1_{\\operatorname{loc}}(\\Omega_T)$, provided $\\epsilon>0$ is small enough. This extends the main result of [V. B\\\"ogelei"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01422","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":""},"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"}