{"paper":{"title":"Existence of solutions to degenerate parabolic problems with two weights via the Hardy inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Anna Zatorska-Goldstein, Iwona Skrzypczak","submitted_at":"2016-11-07T15:46:52Z","abstract_excerpt":"The paper concentrates on the application of the following Hardy inequality \\begin{equation*} \\int_\\Omega \\ |\\xi(x)|^p \\omega_{1 }(x)dx\\le \\int_\\Omega |\\nabla \\xi(x)|^p\\omega_{2 }(x)dx, \\end{equation*} to the proof of existence of weak solutions to degenerate parabolic problems of the type \\begin{equation*} \\left\\{\\begin{array}{ll}\n  u_t-div(\\omega_2(x)|\\nabla u|^{p-2} \\nabla u )= \\lambda W(x) |u|^{p-2}u& x\\in\\Omega,\n  u(x,0)=f(x)& x\\in\\Omega,\n  u(x,t)=0& x\\in\\partial\\Omega,\\ t>0,\\\\ \\end{array}\\right. \\end{equation*} on an open subset $\\Omega\\subseteq\\mathbb{R}^n$, not necessarily bounded, whe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.02125","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"}