{"paper":{"title":"Remarks on a Paper by Leonetti and Siepe","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chao Liu, Hong Tian, Hongya Gao","submitted_at":"2018-12-19T03:25:40Z","abstract_excerpt":"In 2012, F.Leonetti and F.Siepe [1] considered solutions to boundary value problems of some anisotropic elliptic equations of the type $$ \\left\\{ \\begin{array}{llll} \\sum\\limits _{i=1}\\limits^{n} D_i (a_i(x,Du(x)))=0, &x\\in \\Omega,\\\\ u(x)=\\theta (x), & x\\in \\partial \\Omega. \\end{array} \\right. $$ Under some suitable conditions, they obtained an integrability result, which shows that, higher integrability of the boundary datum $\\theta$ forces solutions $u$ to have higher integrability as well. In the present paper, we consider ${\\cal K}_{\\psi,\\theta}^{(p_i)}$-obstacle problems of the nonhomogen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.07740","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"}