{"paper":{"title":"Hardy-type inequality in variable exponent Lebesgue spaces derived from nonlinear problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Iwona Skrzypczak, Sylwia Dudek","submitted_at":"2014-07-23T14:12:39Z","abstract_excerpt":"We derive a family of weighted Hardy-type inequalities in the variable exponent Lebesgue space with an additional term of the form\n  \\[ \\int_\\Omega\\ |\\xi|^{p(x)} \\mu_{1,\\beta}(dx)\\leqslant \\int_\\Omega |\\nabla \\xi|^{p(x)}\\mu_{2,\\beta}(dx)+\\int_\\Omega \\left|\\xi{\\log \\xi} \\right|^{p(x)} \\mu_{3,\\beta}(dx), \\] where $\\xi$ is any compactly supported Lipschitz function. The involved measures depend on a certain solution to the partial differential inequality involving $p(x)$-Laplacian ${-}\\Delta_{p(x)} u\\geqslant \\Phi$, where $\\Phi$ is a given locally integrable function, and $u$ is defined on an ope"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.6226","kind":"arxiv","version":3},"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"}