{"paper":{"title":"Higher Order Calderon-Zygmund Estimates for the p-Laplace Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Anna Kh. Balci, Lars Diening, Markus Weimar","submitted_at":"2019-04-06T08:39:38Z","abstract_excerpt":"The paper is concerned with higher order Calderon-Zygmund estimates for the $p$-Laplace equation $$\n  -\\textrm{div}(A(\\nabla u))\n  := -\\textrm{div}{(|\\nabla\n  u|^{p-2}\\nabla u)}=-\\textrm{div} F, \\qquad 1<p<\\infty. $$ We are able to transfer local interior Besov and Triebel-Lizorkin regularity up to first order derivatives from the force term $F$ to the flux $A(\\nabla u)$. For $p\\geq 2$ we show that $F \\in B^s_{\\rho,q}$ implies $A(\\nabla u) \\in B^s_{\\rho,q}$ for any $s \\in (0,1)$ and all reasonable $\\rho,q \\in (0,\\infty]$ in the planar case. The result fails for $p<2$. In case of higher dimensi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.03388","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"}