{"paper":{"title":"Regularity results for bounded solutions to obstacle problems with non-standard growth conditions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrea Gentile, Andrea Torricelli, Raffaella Giova","submitted_at":"2021-10-18T19:14:09Z","abstract_excerpt":"In this paper we consider a class of obstacle problems of the type\n  %\\begin{equation*} %\\int_{\\Omega}\\left<A(x, Du), D(\\varphi-u)\\right> \\, \\dx\\ge0\\qquad\\forall %\\varphi\\in W^{1,q}(\\Omega) \\quad {\\mathrm{s.t.}} \\quad \\varphi \\ge \\psi %\\end{equation*}\n  \\begin{equation*} \\min \\left\\{\\int_{\\Omega}f(x, Dv)\\, \\dx\\,:\\, v\\in \\mathcal{K}_\\psi(\\Omega)\\right\\} \\end{equation*} where $\\psi$ is the obstacle, $\\mathcal{K}_\\psi(\\Omega)=\\{v\\in u_0+W^{1, p}_{0}(\\Omega, \\R): v\\ge\\psi \\text{ a.e. in }\\Omega\\}$, with $u_0 \\in W^{1,p}(\\Omega)$ a fixed boundary datum, the class of the admissible functions and the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.09586","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/2110.09586/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"}