{"paper":{"title":"A nonexistence result for nonlinear parabolic equations with singular measures as data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Francesco Petitta","submitted_at":"2014-09-30T10:43:54Z","abstract_excerpt":"In this paper we prove a nonexistence result for nonlinear parabolic problems with zero lower order term whose model is $$ \\begin{cases}\n  u_{t}- \\Delta_p u+|u|^{q-1}u=\\lambda & \\text{in}\\ (0,T)\\times\\Omega\n  u(0,x)=0 & \\text{in}\\ \\Omega,\\\\ u(t,x)=0 & \\text{on}\\ (0,T)\\times\\partial\\Omega, \\end{cases} $$ where $\\Delta_p ={\\rm div }(|\\nabla u|^{p-2}\\nabla u)$ is the usual $p$-laplace operator, $\\lambda$ is measure concentrated on a set of zero parabolic $r$-capacity ($1<p<r$), and $q$ is large enough."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.8471","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"}