{"paper":{"title":"Remarks on regularity for $p$-Laplacian type equations in non-divergence form","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Amal Attouchi, Eero Ruosteenoja","submitted_at":"2017-10-20T12:33:06Z","abstract_excerpt":"We study a singular or degenerate equation in non-divergence form modeled by the $p$-Laplacian, $$-|Du|^\\gamma\\left(\\Delta u+(p-2)\\Delta_\\infty^N u\\right)=f\\ \\ \\ \\ \\text{in}\\ \\ \\ \\Omega.$$ We investigate local $C^{1,\\alpha}$ regularity of viscosity solutions in the full range $\\gamma>-1$ and $p>1$, and provide local $W^{2,2}$ estimates in the restricted cases where $p$ is close to 2 and $\\gamma$ is close to 0."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.07506","kind":"arxiv","version":2},"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"}