{"paper":{"title":"Existence to nonlinear parabolic problems with unbounded weights","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Anna Zatorska-Goldstein, Iwona Chlebicka","submitted_at":"2016-11-23T17:54:23Z","abstract_excerpt":"We consider the weighted parabolic problem of the type \\begin{equation*} \\begin{split} \\left\\{\\begin{array}{ll} u_t-\\mathrm{div}(\\omega_2(x)|\\nabla u|^{p-2} \\nabla u )= \\lambda \\omega_1(x) |u|^{p-2}u,& x\\in\\Omega, u(x,0)=f(x),& x\\in\\Omega, u(x,t)=0,& x\\in\\partial\\Omega,\\ t>0, \\end{array}\\right. \\end{split} \\end{equation*} for quite a general class of possibly unbounded weights $ \\omega_1,\\omega_2$ satisfying the Hardy-type inequality. We prove existence of a global weak solution in the weighted Sobolev spaces provided that $\\lambda$ is smaller than the optimal constant in the inequality."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.07904","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"}