{"paper":{"title":"On the notion of renormalized solution to nonlinear parabolic equations with general measure data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessio Porretta, Francesco Petitta","submitted_at":"2015-06-11T13:49:48Z","abstract_excerpt":"Here we introduce a new notion of renormalized solution to nonlinear parabolic problems with general measure data whose model is $$ \\begin{cases} u_t-\\Delta_{p} u =\\mu & \\text{in}\\ (0,T)\\times\\Omega, u=u_0 & \\text{on}\\ \\{0\\} \\times \\Omega, u=0 &\\text{on}\\ (0,T)\\times\\partial\\Omega, \\end{cases} $$ for any, possibly singular, nonnegative bounded measure $\\mu$. We prove existence of such a solutions and we discuss their main properties."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03671","kind":"arxiv","version":2},"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"}